Statistics

### 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...

### 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...

### 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 ∴...

### 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 =...

### 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...

### 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...

### 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.

### 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.

### 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 by students 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,...

### 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...