RD Sharma solutions for Mathematics [English] Class 11 chapter 32 - Statistics [Latest edition]

Calculate the mean deviation about the median of the observation:

3011, 2780, 3020, 2354, 3541, 4150, 5000

Calculate the mean deviation about the median of the observation:

 38, 70, 48, 34, 42, 55, 63, 46, 54, 44

Calculate the mean deviation about the median of the observation:

 34, 66, 30, 38, 44, 50, 40, 60, 42, 51

Calculate the mean deviation about the median of the observation:

 22, 24, 30, 27, 29, 31, 25, 28, 41, 42

Calculate the mean deviation about the median of the observation:

Calculate the mean deviation from the mean for the data: 

 4, 7, 8, 9, 10, 12, 13, 17

Calculate the mean deviation from the mean for the  data:

 13, 17, 16, 14, 11, 13, 10, 16, 11, 18, 12, 17

Calculate the mean deviation from the mean for the  data:

 38, 70, 48, 40, 42, 55, 63, 46, 54, 44a

Calculate the mean deviation from the mean for the  data:

Calculate the mean deviation of the following income groups of five and seven members from their medians:

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2
 Find mean deviation from median

The lengths (in cm) of 10 rods in a shop are given below:
40.0, 52.3, 55.2, 72.9, 52.8, 79.0, 32.5, 15.2, 27.9, 30.2 

In 34, 66, 30, 38, 44, 50, 40, 60, 42, 51 find the number of observations lying between

In  22, 24, 30, 27, 29, 31, 25, 28, 41, 42 find the number of observations lying between 

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.

In 38, 70, 48, 34, 63, 42, 55, 44, 53, 47 find the number of observations lying between

\[\bar { X } \]  − M.D. and

\[\bar { X } \]   + M.D, where M.D. is the mean deviation from the mean.

Calculate the mean deviation from the median of the following frequency distribution:

The number of telephone calls received at an exchange in 245 successive one-minute intervals are shown in the following frequency distribution:

Compute the mean deviation about median.

Calculate the mean deviation about the median of the following frequency distribution:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Find the mean deviation from the median for the  data:

Find the mean deviation from the median for the data: 

Compute the mean deviation from the median of the following distribution:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Find the mean deviation from the mean for the data:

Compute mean deviation from mean of the following distribution:

The age distribution of 100 life-insurance policy holders is as follows:

Calculate the mean deviation from the median age

Find the mean deviation from the mean and from median of the following distribution:

Calculate mean deviation about median age for the age distribution of 100 persons given below:

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

Calculate mean deviation from the median of the following data: 

Find the mean, variance and standard deviation for the data:

 2, 4, 5, 6, 8, 17.

Find the mean, variance and standard deviation for the data:

6, 7, 10, 12, 13, 4, 8, 12.

Find the mean, variance and standard deviation for the data:

 227, 235, 255, 269, 292, 299, 312, 321, 333, 348.

Find the mean, variance and standard deviation for the data 15, 22, 27, 11, 9, 21, 14, 9.

The variance of 15 observations is 4. If each observation is increased by 9, find the variance of the resulting observations.

The mean and standard deviation of 6 observations are 8 and 4 respectively. If each observation is multiplied by 3, find the new mean and new standard deviation of the resulting observations.

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. What are the correct mean and standard deviation?

The mean and standard deviation of 20 observations are found to be 10 and 2 respectively. On rechecking it was found that an observation 8 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 12.

The mean and standard deviation of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations were incorrect, which were recorded as 21, 21 and 18. Find the mean and standard deviation if the incorrect observations were omitted.

Show that the two formulae for the standard deviation of ungrouped data 

\[\sigma = \sqrt{\frac{1}{n} \sum \left( x_i - X \right)^2_{}}\] and 

\[\sigma' = \sqrt{\frac{1}{n} \sum x_i^2 - X^2_{}}\]  are equivalent, where \[X = \frac{1}{n}\sum_{} x_i\]

Find the standard deviation for the following distribution:

Table below shows the frequency f with which 'x' alpha particles were radiated from a diskette 

Find the mean, mode, S.D. and coefficient of skewness for the following data: 

Find the standard deviation for the following data:

Calculate the mean and S.D. for the following data:

Calculate the standard deviation for the following data:

Calculate the A.M. and S.D. for the following distribution:

A student obtained the mean and standard deviation of 100 observations as 40 and 5.1 respectively. It was later found that one observation was wrongly copied as 50, the correct figure being 40. Find the correct mean and S.D.

Calculate the mean, median and standard deviation of the following distribution:

Find the mean and variance of frequency distribution given below:

The weight of coffee in 70 jars is shown in the following table:                                                  

Determine the variance and standard deviation of the above distribution.  

Mean and standard deviation of 100 observations were found to be 40 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.      

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

Calculate the mean, variance and standard deviation of the following frequency distribution. 

Two plants A and B of a factory show following results about the number of workers and the wages paid to them 

The means and standard deviations of heights ans weights of 50 students of a class are as follows: 

Coefficient of variation of two distributions are 60% and 70% and their standard deviations are 21 and 16 respectively. What are their arithmetic means?

Calculate coefficient of variation from the following data:

An analysis of the weekly 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 out larger amount as weekly wages?
(ii) Which firm A or B has greater variability in individual wages?

The following are some particulars of the distribution of weights of boys and girls in a class: 

The mean and standard deviation of marks obtained by 50 students of a class in three subjects, mathematics, physics and chemistry are given below: 

From the data given below state which group is more variable, G₁ or G₂?

Find the coefficient of variation for the following data:

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

Life of bulbs produced by two factories A and B are given below:

The bulbs of which factory are more consistent from the point of view of length of life?  

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? 

If X and Y are two variates connected by the relation

In a series of 20 observations, 10 observations are each equal to k and each of the remaining half is equal to − k. If the standard deviation of the observations is 2, then write the value of k.

If a variable X takes values 0, 1, 2,..., n with frequencies ⁿC₀, ⁿC₁, ⁿC₂ , ... , ⁿC_n, then write variance X.

For a frequency distribution mean deviation from mean is computed by

For a frequency distribution standard deviation is computed by applying the formula

If v is the variance and σ is the standard deviation, then

The mean deviation from the median is

If n = 10, \[X = 12\]   and \[\Sigma x_i^2 = 1530\] , then the coefficient of variation is

The standard deviation of the data:

is

The mean deviation of the series a, a + d, a + 2d, ..., a + 2n from its mean is

A batsman scores runs in 10 innings as 38, 70, 48, 34, 42, 55, 63, 46, 54 and 44. The mean deviation about mean is

The mean deviation of the numbers 3, 4, 5, 6, 7 from the mean is

The sum of the squares deviations for 10 observations taken from their mean 50 is 250. The coefficient of variation is

Let x₁, x₂, ..., x_n be values taken by a variable X and y₁, y₂, ..., y_n be the values taken by a variable Y such that y_i = ax_i + b, i = 1, 2,..., n. Then,

If the standard deviation of a variable X is σ, then the standard deviation of variable \[\frac{a X + b}{c}\] is

If the S.D. of a set of observations is 8 and if each observation is divided by −2, the S.D. of the new set of observations will be

If two variates X and Y are connected by the relation \[Y = \frac{a X + b}{c}\] , where a, b, c are constants such that ac < 0, then

If for a sample of size 60, we have the following information \[\sum_{} x_i^2 = 18000\] and \[ \sum_{} x_i = 960 \] , then the variance is

Let a, b, c, d, e be the observations with mean m and standard deviation s. The standard deviation of the observations a + k, b + k, c + k, d + k, e + k is

The standard deviation of first 10 natural numbers is

Consider the first 10 positive integers. If we multiply each number by −1 and then add 1 to each number, the variance of the numbers so obtained is

Consider the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10. If 1 is added to each number, the variance of the numbers so obtained is

The mean of 100 observations is 50 and their standard deviation is 5. The sum of all squares of all the observations is 

Let x₁, x₂, ..., x_n be n observations. Let  \[y_i = a x_i + b\]  for i = 1, 2, 3, ..., n, where a and b are constants. If the mean of \[x_i 's\]  is 48 and their standard deviation is 12, the mean of \[y_i 's\]  is 55 and standard deviation of \[y_i 's\]  is 15, the values of a and b are 

The mean deviation of the data 3, 10, 10, 4, 7, 10, 5 from the mean is

The mean deviation for n observations \[x_1 , x_2 , . . . , x_n\]  from their mean \[\bar{X} \]  is given by

Let \[x_1 , x_2 , . . . , x_n\]  be n observations and  \[X\]  be their arithmetic mean. The standard deviation is given by

The standard deviation of the observations 6, 5, 9, 13, 12, 8, 10 is