(a) Both Assertion (A) and reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and reason (R) are true and Reason (R) is not a correct explanation of...

### Question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:

(a) Both Assertion (A) and reason (R) are true and Reason (R) is a correct explanation of Assertion (A). (b) Both Assertion (A) and reason (R) are true and Reason (R) is not a correct explanation of...

### Match the following:

### The mean of 2, 7, 6 and x is 15 and mean of 18, 1, 6, x and y is 10. What is the value of y? (a) 5 (b) 10 (c) -20 (d) 30

### If the median of the data 4, 7, x-1, x-3, 16, 25, written in ascending order, is 13 then x is equal to

(a) 13 (b) 14 (c) 15 (d) 16 Answer: (c) 15 Sol: Median of 6 numbers is the average of 3rd and 4th term. ∴ 13 = (????−1)+(????−3) 2 ⇒ 26 = 2x – 4 ⇒ 2x = 30 ⇒ x = 15 Thus, x is equal to...

### The mean of 20 numbers is 0. OF them, at the most, how many may be greater than zero?

(a) 0 (b) 1 (c) 10 (d) 19 Answer: (d) 19 Sol: It is given that mean of 20 numbers is zero. i.e., average of 20 numbers is zero. i.e., sum of 20 numbers is zero. Thus, at most, there can be 19...

### The median of the first 8 prime numbers is

(a) 7 (b) 9 (c) 11 (d) 13 Answer: (b) 9 Sol: First 8 prime numbers are 2, 3, 5, 7, 11, 13, 17 and 19. Median of 8 numbers is average of 4th and 5th terms.

### Look at the cumulative frequency distribution table given below:

Answer: (c) 13 Sol: Converting the given data into a frequency table, we get: Hence, the number of families having an income range of Rs. 20,000 – Rs. 25,000 is 13. The correct option is...

### The median and mode of a frequency distribution are 26 and 29 respectively. Then, the mean is

(a) 27.5 (b) 24.5 (c) 28.4 (d) 25.8 Answer: (b) 24.5 Sol: Mode = (3 × median) – (2 × mean) ⇒ (2 × mean) = (3 × median) – mode ⇒ (2 × mean) = 3 × 26 – 29 ⇒ (2 × mean) = 49 ⇒ Mean = 49 2 ∴ Mean = 24.5...

### The mean and mode of a frequency distribution are 28 and 16 respectively. The median is

(a) 22 (b) 23.5 (c) 24 (d) 24.5 Answer: (c) 24 Sol: Mode = (3 × median) – (2 × mean) ⇒ (3 × median) = (mode + 2 mean) ⇒ (3 × median) = 16 + 56 ⇒ (3 × median) = 72 ⇒ Median = 72 3 ∴...

### Consider the following table:

### Look at the frequency distribution table given below:

### If the mean and median of a set of numbers are 8.9 and 9 respectively, then the mode will be

(a) 7.2 (b) 8.2 (c) 9.2 (d) 10.2 Answer: (c) 9.2 Sol: It is given that the mean and median are 8.9 and 9, respectively, ∴ Mode = (3 × Median) – (2 × Mean) ⇒ Mode = (3 × 9) – (2 × 8.9) = 27 – 17.8 =...

### Median =?

### Mode = ?

### Consider the following frequency distribution

### Consider the frequency distribution of the heights of 60 students of a class

### if the ‘less than type’ ogive and ‘more than type’ ogive intersect each other at (20.5, 15.5) then the median of the given data is

(a) 5.5 (b) 15.5 (c) 20.5 (d) 36.0 Answer: (c) 20.5 Sol: The x- coordinate represents the median of the given data. Thus, median of the given data is 20.5.

### The relation between mean, mode and median is

(a) mode=(3 * mean) – (2 * median) (b) mode=(3 *median) – (2 *mean) (c) median=(3 * mean) – (2 * mode) (d) mean=(3 * median) – (2 *mode) Answer: (b) mode=(3 * median) – (2 *mean) Sol: mode=(3 *...

### While computing the mean of the groue data, we assume that the frequencies are

(a) evenly distributed over the classes (b) centred at the class marks of the classes (c) centred at the lower limits of the classes (d) centred at the upper limits of the classes Answer: (b)...

### In the formula for the following the mean of the grouped data, the i d ’s are the deviations from A of

(a) lower limits of the classes (b) upper limits of the classes (c) midpoints of the classes (d) none of these Answer: (c) midpoints of the classes Sol: The ???????? ′???? are the deviations from A...

### For the finding the mean by using the formula,

### If ‘ i x s are the midpoints of the class intervals of a grouped data, ‘ i f s are the corresponding frequencies and x is the mean then

### The abscissa of the point of intersection of the Less Than Type and of the More Than Type cumulative frequency curves of a grouped data gives its

(a) Mean (b) Median (c) Mode (d)None of these Answer: (b) Median Sol: The abscissa of the point of intersection of the ‘less than type’ and that of the ‘more than type’ cumulative...

### The cumulative frequency table is useful is determining the

(a) Mean (b) Median (c) Mode (d) all of these Answer: (b) Median Sol: The cumulative frequency table is useful in determining the median.

### The medium of a frequency distribution is found graphically with the help of

(a) a histogram (b) a frequency curve (c) a frequency polygon (d) ogives Answer: (d) ogives Sol: This because median of a frequency distribution is found graphically...

### The mode of frequency distribution is obtained graphically from

(a) a frequency curve (b) a frequency polygon (c) a histogram (d) an ogive Answer: (c) a histogram Sol: The mode of a frequency distribution can be obtained graphically from a histogram.

### Which of the following measures of central tendency is influence by extreme values?

(a) Mean (b) Median (c) Mode (d) None of these Answer: (a) Mean Sol: Mean is influenced by extreme values.

### Which of the following cannot be determined graphically?

(a) Mean (b) Median (c) Mode (d) None of these Answer: (a) Mean Sol: The mean cannot be determined graphically because the values cannot be summed.

### Which of the following is not a measure of central tendency?

(a) Mean (b) Mode (c) Median (d) Standard Deviation Answer: (d) Standard Deviation Sol: The standard deviation is a measure of dispersion. It is the action or process of distributing...

### Calculate the missing frequency form the following distribution, it being given that the median of the distribution is 24.

### The following table, construct the frequency distribution of the percentage of marks obtained by 2300 students in a competitive examination.

### The following table gives the life-time (in days) of 100 electric bulbs of a certain brand.

### The following frequency distribution gives the monthly consumption of electricity ofr 64 consumers of locality.

### In the following data, find the values of p and q. Also, find the median class and modal class.

### The following are the ages of 300 patients getting medical treatment in a hospital on a particular day:

### Find the mode of the given data:

### What is the cumulative frequency of the modal class of the following distribution?

### If the median of ???? 5 , ???? 4 , ???? 2 , ???? and ???? 3 , where x > 0, is 8, find the value of x. Hint Arranging the observations in ascending order, we have ????/ 5 , ???? /4 , ????/ 3 , ????/ 2 , ???? Median= ????/ 3 = 8.

### The median of 19 observations is 30. Two more observation are made and the values of these are 8 and 32. Find the median of the 21 observations taken together. Hint Since 8 is less than 30 and 32 is more than 30, so the value of median (middle value) remains unchanged.

Sol: Since, 8 is less than 30 and 32 is more than 30, so the middle value remains unchanged Thus, the median of 21 observations taken together is 30.

### The observation 29, 32, 48, 50, x, x+2, 72, 78, 84, 95 are arranged in ascending order. What is the value of x if the median of the data is 63?arranged in ascending order. What is the value of x if the median of the data is 63?

### In a frequency distribution table with 12 classes, the class-width is 2.5 and the lowest class boundary is 8.1, then what is the upper class boundary of the highest class?

Sol: Upper class boundary = Lowest class boundary + width × number of classes = 8.1 + 2.5×12 = 8.1 + 30 = 38.1 Thus, upper class boundary of the highest class is 38.1.

### The distribution X and Y with total number of observations 36 and 64, and mean 4 and 3 respectively are combined. What is the mean of the resulting distribution X + Y?

### While calculating the mean of a given data by the assumed-mean method, the following values were obtained.

### Find the class marks of classes 10 -25 and 35 – 55.

### Find the class marks of classes 10 -25 and 35 – 55.

### In a class test, 50 students obtained marks as follows:

### For a certain distribution, mode and median were found to be 1000 and 1250 respectively. Find mean for this distribution using an empirical relation.

### A data has 25 observations arranged in a descending order. Which observation represents the median?

### What is the lower limit of the modal class of the following frequency distribution?

### Write the median class of the following distribution:

### From the following data, draw the two types of cumulative frequency curves and determine the median:

### The marks obtained by 100 students of a class in an examination are given below:

### From the following frequency, prepare the ‘more than’ ogive.

### The table given below shows the weekly expenditures on food of some households in a locality

### The following table gives the production yield per hectare of wheat of 100 farms of a village.

### The monthly consumption of electricity (in units) of some families of a locality is given in the following frequency distribution:

### The heights of 50 girls of Class X of a school are recorded as follows:

### Draw a ‘more than’ ogive for the data given below which gives the marks of 100 students.

### The given distribution shows the number of wickets taken by the bowlers in one-day international cricket matches:

### Find the median of the following data by making a ‘less than ogive’.

### The table below shows the daily expenditure on food of 30 households in a locality:

### The following table gives the daily income of 50 workers of a factory:

### A survey regarding the heights (in cm) of 50 girls of a class was conducted and the following data was obtained:

### Find the mean, median and mode of the following data:

### Find the mean, median and mode of the following data:

### Find the mean, median and mode of the following data:

### Find the mean, median and mode of the following data:

### Compute the mode from the following data:

### Compute the mode from the following series:

### Compute the mode from the following data:

### Calculate the mode from the following data:

### Given below is the distribution of total household expenditure of 200 manual workers in a city:

### Find the mode of the following distribution:

### Heights of students of class X are givee in the flowing frequency distribution

### Compute the mode of the following data:

### Find the mode of the following distribution:

### Find the median from the following data:

### Find the median from the following data:

### Find the median wages for the following frequency distribution:

### Calculate the median for the following data:

### If the median of the following frequency distribution is 32.5, find the values of f1 and f2.

### In the following data the median of the runs scored by 60 top batsmen of the world in oneday international cricket matches is 5000. Find the missing frequencies x and yIn the following data the median of the runs scored by 60 top batsmen of the world in oneday international cricket matches is 5000. Find the missing frequencies x and yIn the following data the median of the runs scored by 60 top batsmen of the world in oneday international cricket matches is 5000. Find the missing frequencies x and y

### The median of the following data is 16. Find the missing frequencies a and b if the total of frequencies is 70.

### Calculate the missing frequency from the following distribution, it being given that the median of distribution is 24.

### Calculate the median from the following data:

### Given below is the number of units of electricity consumed in a week in a certain locality:

### Calculate the median from the following frequency distribution table:

### The following table shows the daily wages of workers in a factory:

### Compute mean from the following data:

### In a hospital, the ages of diabetic patients were recorded as follows. Find the median age.

### The following table shows the marks scored by 80 students in an examination:

### Weight of 60 eggs were recorded as given below:

### The following table shows the age distribution of patients of malaria in a village during a particular month:

### Find the mean age from the following frequency distribution:

### Find the mean of the following data using step-deviation method:

### Find the arithmetic mean of the following frequency distribution using step-deviation method:

### In an annual examination, marks (out of 90) obtained by students of Class X in mathematics are given below:

### Find the mean of the following frequency distribution table using a suitable method:

### The weights of tea in 70 packets are shown in the following table:

### Find the mean of the following data, using step-deviation method:

### Find the mean of the following frequency distribution using step-deviation method.

### The following table gives the literacy rate (in percentage) in 40 cities. Find the mean literacy rate, choosing a suitable method.

### Find the mean of the following data, using assumed-mean method:

### Find the mean of the following frequency distribution, using the assumed-mean method:

### Find the mean marks per student, using assumed-mean method:

### During a medical check-up, the number of heartbeats per minute of 30 patients were recorded and summarized as follows:

### Find the mean of the following frequency distribution is 57.6 and the total number of observation is 50.

### The daily expenditure of 100 families are given below. Calculate ????1 and ????2 if the mean daily expenditure is ₹ 188.

### The mean of the following frequency data is 42, Find the missing frequencies x and y if the sum of frequencies is 100.

### The mean of following frequency distribution is 54. Find the value of p.

### The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is ₹ 18 , find the missing frequency f.

### If the mean of the following frequency distribution is 24, find the value of p.

### Using an appropriate method, find the mean of the following frequency distribution:

### Find the mean of the following data, using direct method:

### Find the mean of the following data, using direct method:

### Find the mean using direct method:

### Compute the mean for following data:

### If the mean of 25 observations is 27 and each observation is decreased by 7, what will be new mean?

### If the mean of 5 observation x, x + 2, x + 4, x +6and x + 8 , find the value of x.

### While calculating the mean and variance of 10 readings, a student wrongly used the reading 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.

Solution: Given that $n=10, \bar{x}=45$ and $\sigma^{2}=16$ $\begin{array}{l} \bar{x}=45 \Rightarrow \frac{\Sigma x_{i}}{n}=45 \\ \Rightarrow \quad \frac{\Sigma x_{i}}{10}=45 \Rightarrow \Sigma...

### Mean and standard deviation of 100 observations were found to be and 10, respectively. If at the time of calculation two observations were wrongly taken as 30 and 70 in place of 3 and 27 respectively, find the correct standard deviation.

Solution: Provided, $n=100, \bar{x}=40$ and $\sigma=10$ $\begin{array}{ll} \therefore \quad & \frac{\Sigma x_{i}}{n}=40 \\ \Rightarrow \quad & \frac{\Sigma x_{i}}{100}=40 \\ \Rightarrow...

### Following are the marks obtained, out of 100 , by two students Ravi and Hashina in 10 tests.

Who is more intelligent and who is more consistent?

Solution: For Ravi $$\begin{tabular}{|c|c|c|} \hline$x_{i}$ & $d_{i}=x_{i}-45$ & $d_{i}^{2}$ \\ \hline 25 & $-20$ & 400 \\ \hline 50 & 5 & 25 \\ \hline 45 & 0 & 0 \\ \hline 30 & $-15$ & 225 \\...

### Determine mean and standard deviation of first terms of an A.P. whose first term is a and common difference is .

Solution: Given that the first $n$ terms of an A.P. whose first term is a and common difference is d Now we have to find mean and standard deviation Given AP in tabular form is shown below,...

### The weights of coffee in 70 jars are shown in the following table:

Determine variance and standard deviation of the above distribution.

Solution: The weights of coffee in 70 jars is given We now need to find the variance and standard deviation of the distribution Let's construct a table of the given data and append other columns...

### Calculate the mean deviation about the mean for the following frequency distribution:

Solution: The frequency distribution is given We now need to find the mean deviation about the mean Let's construct a table of the given data and append other columns after calculations...

### Find the mean and variance of the frequency distribution given below:

Solution: The frequency distribution is given We now need to find the mean and variance Convert the ranges of $x$ to groups, we can re-write the given table as shown below,...

### If for a distribution and the total number of item is 18 , find the mean and standard deviation.

Solution: Provided that for a distribution $\sum(x-5)=3, \sum(x-5)^{2}=43$ and the total number of item is 18 Now we have to find the mean and standard deviation. As per the criteria given No. of...

### Mean and standard deviation of 100 items are 50 and 4, respectively. Find the sum of all items and the sum of the squares of the items.

Solution: It is given that mean and standard deviation of 100 items are 50 and 4, respectively We now need to find the sum of all items and the sum of the squares of the items As per the criteria...

### The mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7 hours. Find the overall standard deviation.

Solution: Given that the mean life of a sample of 60 bulbs was 650 hours and the standard deviation was 8 hours. A second sample of 80 bulbs has a mean life of 660 hours and standard deviation 7...

### There are 60 students in a class. The following is the frequency distribution of the marks obtained by the students in a test:

Where is a positive integer. Determine the mean and standard deviation of the marks.

Solution: It is given that there are 60 students in a class. Also the frequency distribution of the marks obtained by the students in a test is given. We now need to find the mean and the standard...

### For the frequency distribution:

Find the standard distribution.

Solution: Provided: frequency distribution table We now need to find the standard deviation Let's construct a table of the data given and append other columns after calculations...

### The frequency distribution:

Where is a positive integer, has a variance of Determine the value of .

Solution: In the given frequency distribution table, where variance $=160$ We now need to find the value of $A$, where $A$ is a positive number We need to construct a table of the data given...

### Two sets each of 20 observations have the same standard derivation 5 . The first set has a mean 17 and the second a mean 22. Determine the standard deviation of the set obtained by combining the given two sets.

Solution: Provided: Two sets each of 20 observations, have the same standard derivation 5 . The first set has a mean 17 and the second a mean $22 .$ We now need to show that the standard deviation...

### The mean and standard deviation of a set of observations are and , respectively while the mean and standard deviation of another set of observations are and , respectively. Show that the standard deviation of the combined set of observations is given by

S.D.

Solution: The variance $\sigma^{2}$ of the combined series is given by...

### The mean and standard deviation of some data for the time taken to complete a test are calculated with the following results: Number of observations , mean seconds, standard deviation seconds. Further, another set of 15 observations , also in seconds, is now available and we have

and

Calculate the standard derivation based on all 40 observations.

Solution: Provided: No. of observations $=25$, mean $=18.2$ seconds, standard deviation = $3.25$ seconds. Another set of 15 observations $x_{1}, x_{2}, \ldots, x_{15}$, also in seconds, is...

### Find the standard deviation of the first n natural numbers.

Solution: It is given: set of first $n$ natural numbers We now need to find the standard deviation Provided first $n$ natural numbers, it can be written in table as shown below...

### Calculate the mean deviation about the mean of the set of first natural numbers when is an even number.

Solution: It is given that set of first $n$ natural numbers when $\mathrm{n}$ is an even number. We now need to find the mean deviation about the mean It is known that the first $n$ natural numbers...

### Calculate the mean deviation about the mean of the set of first natural numbers when is an odd number.

Solution: It is given that the set of the first $n$ natural numbers when $n$ is an odd number. We now need to find the mean deviation about the mean. It is known that first $n$ natural numbers are...

### Find the mean deviation about the median of the following distribution:

Solution: Data distribution is given We now need to find the mean deviation about the median Construct a table of the given data and append other columns after calculations...

### Find the mean deviation about the mean of the distribution:

Solution: Data distribution is given We now need to find the mean deviation about the mean of the distribution. Draw a table of the data given. $$\begin{tabular}{|l|l|l|} \hline Size...

### For each of the following compound statements first identify the connecting words and then break it into component statements. (i) All rational numbers are real and all real numbers are not complex. (ii) Square of an integer is positive or negative.

(I) In this sentence 'and' is the associating word The part proclamations are as per the following (a) All normal numbers are genuine (b) All genuine numbers are not perplexing (ii) In this...

**The distributions of below give a weight of 30 students of a class. Find the median weight of a student.**

Weight(in kg)40-4545-5050-5555-6060-6565-7070-75Number of students2386632 Solution: Class Interval Frequency ...

**In this 100 surnames were randomly picked up from a local telephone directory and the frequency distribution of the number of letters in English alphabets in the surnames was obtained as follows:**

Number of letters1-44-77-1010-1313-1616-19Number of surnames630401644 Determine the number of median letters in the surnames. Find the number of mean letters in the surnames and also, find the size...

**The following table gives the distribution of a life time of 400 neon lamps.**

Lifetime (in hours)Number of lamps1500-2000142000-2500562500-3000603000-3500863500-4000744000-4500624500-500048 Find the median lifetime of a lamp. Solution: Class...

**The lengths of 40 leaves in a plant are measured correctly to the nearest millimeter, and the data obtained is represented as in the following table:**

Length (in mm)Number of leaves118-1263127-1355136-1449145-15312154-1625163-1714172-1802 Find the median length of leaves. solution: Since the information are not ceaseless diminish 0.5 in as far as...

**5. The following distribution gives the daily income of workers of a factory:**

Daily income (in Rs):No of workers:100 – 12012120 – 14014140 – 1608160 – 180 6180 – 20010 Convert the above distribution to a ‘less than’ type...

**4. The monthly profits (in Rs) of shops are distributed as follows:**

Profit per shopNo of shops:0 – 50 1250 – 10018100 – 15027150 – 20020200 – 25017250 – 3006 Draw the frequency polygon for it. Solution: Statistics is the discipline...

**3. Draw an Ogive to represent the following frequency distribution:**

Class-interval0 – 45 – 910 – 1415 – 1920 – 24No. of students261053...

**2. The marks scored bystudents in an examination are given in the form of a frequency distribution table:**

MarksNo. of Students600 – 640 16640 – 68045680 – 720156720 – 760284760 – 800172800 – 84059840 – 88018 Solution: Statistics is the discipline that concerns the...

**2. The shirt size worn by a group of persons, who bought the shirt from a store, are as follows:**

Shirt size:3738394041424344Number of persons:1525394136171512 Solution: Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data....

**3. Find the mode of the following distribution.**

(i) Class interval:0 – 1010 – 2020 – 3030 – 4040 – 5050 – 6060 – 7070 – 80Frequency:5871228201010 Solution Statistics is the discipline that concerns the collection, organization, analysis,...

**4. Compare the modal ages of two groups of students appearing for an entrance test:**

Age in years16 – 1818 – 2020 – 2222 – 2424 – 26Group A5078462823Group B5489402517 Solution Statistics is the discipline that concerns the collection, organization, analysis, interpretation, and...

**1. Find the mode of the following data: **

(i) $3,5,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4$ (ii) $3,3,7,4,5,3,5,6,8,9,5,3,5,3,6,9,7,4$ (iii) $15,8,26,25,24,15,18,20,24,15,19,15$ Solution: Statistics is the...

**5. The marks in science of students of class X are given below. Find the mode of the marks obtained by the students in science.**

Marks0 – 1010 – 2020 – 3030 – 4040 – 5050 – 6060 – 7070 – 8080 – 9090 – 100Frequency35161213205411 Solution Statistics is the discipline that concerns the collection, organization, analysis,...

### 7. Find the lost frequency for giving distribution, mean is

$x:$$3$$5$$7$$9$$11$$13$$f:$$6$$8$$15$$p$$8$$4$ Solution: $x$$f$$fx$$3$$6$$18$$5$$8$$40$$7$$15$$105$$9$$p$$9p$$11$$8$$88$$13$$4$$52$$N=41+p$$\sum{fx=303+9p}$ We know that, Mean $=\sum{fx/N=\left(...

### 6. Find the missing value of for the given distribution whose mean is

$x:$$5$$8$$10$$12$$p$$20$$25$$f:$$2$$5$$8$$22$$7$$4$$2$ Solution: $x$$f$$fx$$5$$2$$10$$8$$5$$40$$10$$8$$80$$12$$22$$264$$P$$7$$7p$$20$$4$$80$$25$$2$$50$$N=50$$\sum{fx=524+7p}$ We know that, Mean...

### 5. Find the value of for the given distribution whose is mean

$x:$$8$$12$$15$$p$$20$$25$$30$$f:$$12$$16$$20$24$16$$8$$4$ Solution: $x$$f$$fx$$8$$12$$96$$12$$16$$192$$15$$20$$300$$P$$24$$24p$$20$$16$$320$$25$$8$$200$$30$$4$$120$$N=100$$\sum{fx=1228+24p}$ We...

### 2. The following is the distribution of height of students of a certain class in a certain city:

Find the median height. Solution: Here, we have N = \[420,\] So\[,\text{ }N/2\text{ }=\text{ }420/\text{ }2\text{ }=\text{ }210\] The cumulative frequency just greater than \[N/2\text{ }is\text{...

### 4. If the mean of the given data is , find

$x:$$5$10$15$$20$$25$$f:$$6$$p$$6$$10$$5$ Solution: $x$$f$$fx$$5$$6$$30$$10$$p$$10p$$15$$6$$90$$20$$10$$200$$25$$5$$125$$N=p+27$$\sum{fx=445+10p}$ We know that, Mean $=\sum{fx/N=\left( 445+10p...

### 3. If is the mean of given data. Find the value of

$x:$$10$$15$$p$$25$$35$$f:$$3$$10$$25$$7$$5$ Solution: $x$$f$$fx$$10$$3$$30$$15$$10$$150$$p$$25$$25p$$25$$7$$175$$35$$5$$175$$N=50$$\sum{fx=530+25p}$ We know that, Mean $=\sum{fx/N=\left( 2620+25p...

### 2. Find the mean of the given data:

$x:$$19$$21$$23$$25$$27$$29$$31$$f:$$13$$15$$16$$18$$16$$15$$13$ Solution: $x$$f$$fx$$19$$13$$247$$21$$15$$315$$23$$16$$368$$25$$18$$450$$27$$16$$432$$29$$15$$435$$31$$13$$403$$N=106$$\sum{fx}=2620$...

**The Life insurance agent found the following data for the distribution of ages of 100 policy holders. Calculate the median age, if policies are given only to the persons whose age is 18 years onwards but less than the 60 years.**

Age (in years)Number of policy holderBelow 202Below 256Below 3024Below 3545Below 4078Below 4589Below 5092Below 5598Below 60100 Solution: Class interval ...

**2. If the median of a distribution given below is 28.5 then, find the value of x & y.**

Class IntervalFrequency0-10510-20x20-302030-401540-50y50-605Total60 Arrangement: Given information, n = 60 Middle of the given information = 28.5 Where, n/2 = 30 Middle class is 20 – 30 with an...

**The following frequency distribution gives the monthly consumption of an electricity of 68 consumers in a locality. Find the median, mean and mode of the data and compare them.**

Monthly consumption(in units)No. of customers65-85485-1055105-12513125-14520145-16514165-1858185-2054 Solution: Track down the aggregate recurrence of the given information as follows: Class...

**6. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data:**

Number of carsFrequency0-10710-201420-301330-401240-502050-601160-701570-808 solution Given Data: Modular class = 40 – 50, l = 40, Class width (h) = 10, fm = 20, f1 = 12 and f2 = 11 \[Mode\text{...

**5. The given distribution shows the number of runs scored by some top batsmen of the world in one- day international cricket matches.**

Run ScoredNumber of Batsman3000-400044000-5000185000-600096000-700077000-800068000-900039000-10000110000-110001 Find the mode of the data. Solution: Given information: Modular class = 4000 – 5000, l...

**4. The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. Find the mode and mean of this data. Interpret the two measures**

No of Students per teacherNumber of states / U.T15-20320-25825-30930-351035-40340-45045-50050-552 Solution: Given information: Modular class = 30 – 35, l = 30, Class width (h) = 5, fm = 10, f1 = 9...

**3. The following data gives the distribution of total monthly household expenditure of 200**

families of a village. Find the modal monthly expenditure of the families. Also, find the

mean monthly expenditure:

families of a village. Find the modal monthly expenditure of the families. Also, find the

mean monthly expenditure:

ExpenditureNumber of families1000-1500241500-2000402000-2500332500-3000283000-3500303500-4000224000-4500164500-50007 Solution: From the given information the modular class is 60–80. l = 60, The...

**2. The following data gives the information on the observed lifetimes (in hours) of 225**

electrical components:

electrical components:

Lifetime (in hours)0-2020-4040-6060-8080-100100-120Frequency103552613829 Determine the modal lifetimes of the components. Solution: From the given information the modular class is 60–80. l = 60, The...

**1. The following table shows the ages of the patients admitted in a hospital during a year:**

Age (in years)5-1515-2525-3535-4545-5555-65Number of patients6112123145 Find the mode and the mean of the data given above. Compare and interpret the twomeasures of central tendency. Solution: To...

**9. The following table gives the literacy rate (in percentage) of 35 cities. Find the mean**

literacy rate.

literacy rate.

Literacy rate (in %)45-5555-6565-7575-8585-98Number of cities3101183 Solution: Discover the midpoint of the given stretch utilizing the recipe. Midpoint (xi) = (maximum cutoff + lower limit)/2 For...

### A class instructor has the accompanying truant record of 40 understudies of a class for the entirety term. Track down the mean number of days an understudy was missing. 0-6 6-10 10-14 14-20 20-28 28-38 38-40 Number of students 11 10 7 4 4 3 1

Arrangement: Discover the midpoint of the given stretch utilizing the equation. Midpoint (xi) = (maximum cutoff + lower limit)/2 Class interval Frequency (fi) Mid-point (xi) fixi 0-6 11 3 33 6-10 10...

### To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below:

Concentration of SO2 ( in ppm)Frequency0.00 – 0.0440.04 – 0.0890.08 – 0.1290.12 – 0.1620.16 – 0.2040.20 – 0.242 Find the mean concentration of SO2 in the air. SOLUTION To discover the mean,...

**The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.**

Daily expenditure(in c)100-150150-200200-250250-300300-350Number of households451222 Solution: Discover the midpoint of the given span utilizing the recipe. \[Midpoint\text{ }\left( xi \right)\text{...

**In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes.**

Number of mangoes50-5253-5556-5859-6162-64Number of boxes1511013511525 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose? Solution: Since, the...

### Thirty ladies were analyzed in a medical clinic by a specialist and the quantity of heart beats each moment were recorded and summed up as follows. Track down the mean heart beats each moment for these ladies, picking an appropriate strategy. Number of heart beats per minute 65-68 68-71 71-74 74-77 77-80 80-83 83-86 Number of women 2 4 3 8 7 4 2

solution: From the given information, let us expect the mean as A = 75.5 \[xi\text{ }=\text{ }\left( Upper\text{ }cutoff\text{ }+\text{ }Lower\text{ }limit \right)/2\] Class size (h) = 3 Presently,...

### The accompanying dissemination shows the day by day pocket stipend of offspring of a territory. The mean pocket remittance is Rs 18. Track down the missing recurrence .

solution: To discover the missing recurrence, utilize the mean equation. Here, the worth of mid-point $\left(\mathrm{x}_{\mathrm{i}}\right)$ mean $\overline{\mathrm{x}}=18$

### Think about the accompanying dispersion of day by day wages of 50 specialists of a processing plant.

\begin{tabular}{|l|l|l|l|}

Day by day compensation (in Rs.) and and and and and \

\hline

\end{tabular}

\begin{tabular}{|l|l|}

\hline Number of laborers and 12 \

\hlineend{tabular}Track down the mean day by day wages of the laborers of the production line by utilizing a proper strategy.

14 8 ( 10 Solution: Discover the midpoint of the given span utilizing the recipe. Midpoint $\left(\mathrm{x}_{\mathrm{i}}\right)=($ maximum breaking point $+$ lower limit $)/2$ For this situation,...

### During the clinical examination of 35 understudies of a class, their loads were recorded as follows: Draw a not as much as type ogive for the given information. Henceforth get the middle load from the chart and confirm the outcome by utilizing the equation.

Solution: From the offered information, to address the table as chart, pick the maximum furthest reaches of the class stretches are in $x$-hub and frequencies on $\mathrm{y}$-pivot by picking the...

### The accompanying appropriation gives the every day pay of 50 laborers if a plant. Convert the appropriation above to a not as much as type aggregate recurrence circulation and draw its ogive. Every day pay in Rupees 100-120 120-140 140-160 160-180 180-200 Number of workers 12 14 8 6 10

Solution: Convert the given appropriation table to a not as much as type aggregate recurrence circulation, and we get Every day income Frequency Cumulative Frequency Under 120 12 12 Under 140 14 26...

### The accompanying tables gives creation yield per hectare of wheat of 100 homesteads of a town. Creation Yield 50-55 55-60 60-65 65-70 70-75 75-80 Number of farms 2 8 12 24 38 16 change the dispersion to a more than type dissemination and draw its ogive.

Solution: Changing the given dissemination over to a more than type conveyance, we get Creation Yield (kg/ha) Number of ranches More than or equivalent to 50 100 More than or equivalent to 55 100-2...

### An overview was led by a gathering of understudies as a piece of their current circumstance mindfulness program, in which they gathered the accompanying information in regards to the quantity of plants in 20 houses in an area. Track down the mean number of plants per house. Number of Plants 0-2 2-4 4-6 6-8 8-10 10-12 12-14 Number of Houses 1 2 1 5 6 2 3 Which technique did you use for tracking down the mean, and why?

Solution: To track down the mean worth, we will utilize direct technique in light of the fact that the mathematical worth of fi and xi are little. Discover the midpoint of the given stretch...