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Class: | 11 |

Subject: | Maths |

Chapter 15: | Statistics |

Table of Contents

## NCERT Solutions for Class 11 Maths Chapter 15

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### Class 11 Maths Chapter 15 Statistics Solutions

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#### Important Questions on Statistics

- The variance of 10 observations is 16 and their mean is 12. If each observation is multiplied by 4, what are the new mean and the new variance? [Answer: 48, 256]
- Find the mean deviation from the mean of A.P: a, a + d, a + 2d… a + 2nd. [Answer: {n(n + 1)/(2n + 1)}d]
- Mean and standard deviation of the data having 18 observations were found to be 7 and 4 respectively. Later it was found that 12 was wrongly copied as 21 in calculation. Find the correct mean and the correct standard deviation. [Answer: 6.5, 2.5]

##### Questions for Practice

- Consider the first 10 positive integers. If we multiply each number by –1 and then add 1 to each number, find the variance of the numbers so obtained. [Answer: 8.25]
- 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 correct standard deviation. [Answer: 10.24]
- Coefficients of variation of two distributions are 60 and 80 and their standard deviations are 21 and 36. What are their means? [Answer: 35, 45]

###### Try These

- The standard deviation of 25 observations is 4 and their mean is 25. If each observation is increased by 10, what are the new mean and the new standard deviation? [Answer: 35, 4]
- The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1, 2 and 6. Find the other two observations. [Answer: 4, 9]
- In a series of 2n observations, half of them equal ‘a’ and remaining half equal –a. If the standard deviation of the observations is 2, then find the value of |a|. [Answer: 2]

Table of Contents

#### What are the main methods of measures of dispersion?

The dispersion or scatter in a data is measured on the basis of the observations and the types of the measure of central tendency, used there.

There are following measures of

dispersion:

(i) Range,

(ii) Quartile deviation,

(iii) Mean deviation,

(iv) Standard deviation.

There are following measures of

dispersion:

(i) Range,

(ii) Quartile deviation,

(iii) Mean deviation,

(iv) Standard deviation.

#### What is mean Deviation?

The mean deviation about a central value ‘a’ is the mean of the absolute values of the deviations of the observations from ‘a’. The mean deviation from ‘a’ is denoted as M.D. (a).

#### What do you mean by standard deviation?

The proper measure of dispersion about the mean of a set of observations is expressed as positive square-root of the variance and is called standard deviation. Therefore, the standard deviation, usually denoted by σ.