Solution:- Calculate Mean for Length x,

### The sum and sum of squares corresponding to length x (in cm) and weight y (in gm) of

### The following is the record of goals scored by team A in a football session: For the team B, mean number of goals scored per match was

with a standard deviation

goals. Find which team may be considered more consistent?

Solution:- According to the given data, Draw the table of the given data and append other columns after calculations. Since C.V. of firm B is greater Therefore, Team A is more consistent....

### An analysis of monthly wages paid to workers in two firms A and B, belonging to the same industry, gives the following results: (i) Which firm A or B pays larger amount as monthly wages? (ii) Which firm, A or B, shows greater variability in individual wages?

Solution:- (i) According to the given table, Mean monthly wages of firm A = Rs \[5253\] and Number of wage earners = \[586\] Then, Total amount paid = \[586\text{ }\times \text{ }5253\] = Rs...

### From the prices of shares X and Y below, find out which is more stable in value:

Solution:- From the given data, draw the table of the given data and append other columns after calculations. Now calculate Mean for x, Mean $\bar{X}=\sum {{x}_{i}}/n$ Where, n =...

### From the data given below state which group is more variable, A or B?

Solution:- Calculate the coefficient of variance for each series for comparing the variability or dispersion of two series. The series having greater C.V. is said to be more variable than the other....

### The diameters of circles (in mm) drawn in a design are given below:

Calculate the standard deviation and mean diameter of the circles. [Hint first make the data continuous by making the classes as \[32.5-36.5,36.5-40.5,40.5-44.5,44.5-48.5,48.5-52.5\] and then...

### Find the mean, variance and standard deviation using short-cut method

Solution:- Let us consider assumed mean, A = \[92.5\] and h = \[5\] Draw the table of the given data and append other columns after calculations. Mean,...

### Find the mean and variance for the following frequency distributions

Solution:- Draw the table of the given data and append other columns after calculations.

### Find the mean and variance for the following frequency distributions

Solution:- Draw the table of the given data and append other columns after calculations.

### Find the mean and standard deviation using short-cut method.

Solution:- Let us consider the assumed mean A = \[64\]. Here h = \[1\] Mean, \[\bar{X}=A+\frac{\sum\limits_{i=1}^{a}{{{f}_{i}}{{y}_{i}}}}{N}\times h\] Where A = \[64\], h = \[1\]...

### Find the mean and variance for each of the data

Solution:- Draw the table of the given data and append other columns after calculations.

### Find the mean and variance for each of the data

Solution:- Draw the table of the given data and append other columns after calculations.

### Find the mean and variance for each of the data First

multiples of

Solution:- Let us take \[10\] multiples of \[3\] are \[3,6,9,12,15,18,21,24,27,30\] We know that Mean = \[\bar{X}=\sum\limits_{i=1}^{a}{{{x}_{i}}}\]...

### Is it true that for any sets A and B, P (A) ∪ P (B) = P (A ∪ B)? Justify your answer.

Solution: No, it is not true that for any sets $A$ and $B, P(A) \cup P(B)=P(A \cup B)$ Justification: Let's suppose, $A=\{0,1\}$ And, $B=\{1,2\}$ $\therefore \text{ }A~\cup ~B~=\text{ }\left\{...

### Find the mean and variance for each of the data First n natural numbers

Solution:- As Mean = Sum of all observations/Number of observations ∴Mean, \[\bar{X}=((n(n+1))2)/n\] = \[(n+1)/2\] and also for Variance, \[{{\sigma...

### Find the mean and variance for each of the data.

Solution:- Given \[6,7,10,12,13,4,8,12\] Mean = \[\bar{X}\]= \[\frac{1}{n}\sum\limits_{i=1}^{a}{{{x}_{i}}}\](n=number of observation) \[\sum\limits_{i=1}^{a}{{{x}_{i}}}\]= sum of total observation...

### Calculate the mean deviation about median age for the age distribution of

persons given below: [Hint Convert the given data into continuous frequency distribution by subtracting

from the lower limit and adding

to the upper limit of each class interval]

Solution:- The given data is converted into continuous frequency distribution by subtracting \[0.5\] from the lower limit and adding the \[0.5\] to the upper limit of each class intervals and append...

### Find the mean deviation about median for the following data:

Solution:- Draw the table of the given data and append other columns after calculations. The class interval containing \[{{N}^{th}}/2\]or \[25\] item is \[20-30\] So, \[20-30\]is the median class....

### Find the mean deviation about the mean for the data

Solution:- Draw a table of the given data and append other columns after calculations. The sum of calculated data, N= \[\sum\limits_{i=1}^{6}{{{f}_{i}}=100}\],...

### Find the mean deviation about the mean for the data

Solution:- Draw a table of the given data and append other columns after calculations. The sum of calculated data, N= \[\sum\limits_{i=1}^{8}{{{f}_{i}}=50}\],...

### Find the mean deviation about the median for the data

Solution:- Draw a table of the given data and append other columns after calculations. Now, N = 29, which is odd. The cumulative frequency greater than \[14.5\] is \[21\], for which the...

### Find the mean deviation about the median for the data.

Solution:- Draw a table of the given data and append other columns after calculations. We know that, N = \[26\], which is even. So, median is the mean of the \[13\]and \[14\] observations. Both of...

### Find the mean deviation about the mean for the data

Solution:- Draw a table of the given data and append other columns after calculations. The sum of calculated data, N = \[\sum\limits_{i=1}^{5}{{{f}_{i}}}=80\],...

### Find the mean deviation about the mean for the data

\[{{x}_{i}}\] \[5\] \[10\] \[15\] \[20\] \[25\] \[{{f}_{i}}\] \[7\] \[4\] \[6\] \[3\] \[5\] Solution:- We have to make the table of the given data and append other columns after calculations....

### Find the mean deviation about the median for the data.

Solution:- To find the median arrange the given observations in ascending order, \[36,42,45,46,46,49,51,53,60,72\] Total number of observations = \[10\] Then, Median = (\[{{(10/2)}^{th}}\]...

### Find the mean deviation about the median for the data.

Solution:- To find the median arrange the given observations in ascending order, \[10,11,11,12,13,13,14,16,16,17,17,18\] Total number of observations = \[12\] Then, Median = (\[{{(12/2)}^{th}}\]...

### Find the mean deviation about the mean for the data.

,

,

,

,

,

,

,

,

,

Solution:- To find mean deviation, first we have to find mean\[(\overline{x})\] \[\overline{x}=\frac{1}{10}\sum\limits_{i=1}^{10}{{{x}_{i}}}=\frac{500}{10}=50\] Determine the respective values of...

### Find the mean deviation about the mean for the data.

,

,

,

,

,

,

,

Solution:- Given data \[4\], \[7\], \[8\], \[9\], \[10\], \[12\], \[13\], \[17\] To find mean deviation, first we have to find mean\[(\overline{x})\]...

### The mean and standard deviation of a group of observations were found to be and , respectively. Later on it was found that three observations were incorrect, which were recorded as , and . Find the mean and standard deviation if the incorrect observations are omitted.

We are given, The total number of observations, $n = 100$. Incorrect mean, $\overline x = 20$. And, Incorrect standard deviation, $\sigma = 3$. So, Mean is given by, $\overline {\text{X}} =...

### The mean and standard deviation of marks obtained by students of a class in three subjects, Mathematics, Physics and Chemistry are given below. Which of the three subjects shows the highest variability in marks and which shows the lowest?

We are given, The mean and standard deviation of Mathematics are $42$and $12$ respectively. The mean and standard deviation of Physics are $32$ and $15$ respectively. The mean and standard deviation...

### The mean and standard deviation of observations are found to be and , respectively. On rechecking, it was found that an observation was incorrect. Calculate the correct mean and standard deviation in each of the following cases: (i) If wrong item is omitted. (ii) If it is replaced by .

(i) When the wrong item is omitted, We are given, The number of observations, $n = 20$. The mean before rechecking $ = 10$. The standard deviation before rechecking $ = 2$. Mean is given by,...

### Given that is the mean and is the variance of observations , , …., . Prove that the mean and variance of the observations , , , …., are and , respectively, ().

We are given $n$ observations ${x_1}$, ${x_2}$, …., ${x_n}$ . Mean of $n$ observations $ = \overline x $. Variance of $n$ observations $ = {\sigma ^2}$. Also, we have variance, $\sigma = \sqrt...

### The mean and standard deviation of six observations are and , respectively. If each observation is multiplied by , find the new mean and new standard deviation of the resulting observations.

We are given that, The mean of six observations $ = 8$. The standard deviation of six observations $ = 4$. Let us consider the six observations as ${x_1}$, ${x_2}$, ${x_3}$, ${x_4}$, ${x_5}$ and...

### The mean and variance of observations are and respectively. If five of the observations are , , , . . Find the remaining two observations.

We are given, the mean and variance of eight observations are $8$ and $16$ respectively. Also, we have five observations $2$, $4$, $10$, $12$ and $14$. Suppose that the remaining two observations to...

### The mean and variance of eight observations are and , respectively. If six of the observations are , , , , and , find the remaining two observations.

We are given, the mean and variance of eight observations are $9$ and $9.25$ respectively. Also, we have six observations $6$, $7$, $10$, $12$, $12$ and $13$. Suppose that the remaining two...