## Kerala Plus One Maths Chapter Wise Questions and Answers Chapter 15 Statistics

**Short Answer** **Type Questions **

**(Score 3)**

Question 1.

a. Coefficient of variation is computed by

b. If in a frequency distribution, the mean and median are 21 and 22 respectively, then find its mode is approximately.

Answer:

b. 24.0

Mode ± 2 mean = 3 median

Mode = 3 median -2 mean

= 3 × 22-2 × 21 =66-42 = 24

Question 2.

a. Which of the following is not a measure of dispersion?

a. mean

b. variance

c. mean deviation

d. range

b. Find the variance of 2,4,6,8,10.

Answer:

a. mean

Question 3.

Find the mean deviation (about mean) of the following data.

6,9,10,12,2,3,5,17,20,26.

Answer:

Question 4.

Consider the following data:

3,9,5,3,12,10,18,4,7,19,21

i. The median of the above data is…….

ii. Find the mean deviation from the median.

Answer:

i. 9

Question 5.

For the following observations:

28,36,34, 28,48, 22,35,27,19,41

Find the arithmetic mean and median. Also find the variance.

Answer:

=31.8 Median = 31

σ^{2} = 69.16

Question 6.

The scores of 10 players in a game are given below:

42, 52,55,72, 52, 79,32,15,27,30.

i. Find the mean.

ii. Find the mean deviation from the mean.

Answer:

Question 7.

Consider the following data:

65, 58,68,44,48,45,60,62,60, 50

i. Find the mean of the data.

ii. Calculate the variance.

Answer:

Question 8.

Consider the following data:

i. Find the median of the data.

ii. Calculate

iii. Calculate mean deviation from the median.

Answer:

i. Median = 13

ii. 149

iii. M.D = (M) = 149/30 = 4.97

**Short Answer** **Type Questions **

**(Score 4)**

Question 1.

Marks obtained in Mathematics examination are given below:

i. Mean of the marks =……………..

ii. Find variance of the marks.

iii. Find standard deviation of marks.

Answer:

i. Mean of the marks = 22.5

Question 2.

a. Find the mean deviation from the median for the following data:

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

b. Find the mean deviation from the mean for the following observation:

9,21,3,10,5,12,3,18,21,8

Answer:

Question 3.

Scores obtained by 10 students in English and Mathematics are displayed here

English(out of 50) | Maths(out of 50) |

20 | 25 |

28 | 35 |

12 | 33 |

48 | 37 |

37 | 20 |

43 | 38 |

14 | 40 |

18 | 21 |

48 | 29 |

32 | 22 |

i. Calculate arithmetic mean of scores in English.

ii. Compare the arithmetic means of scores in English and Mathematics.

iii. Comment on the scattering or spreading of the above data (scores in English and scores in Maths) using standard deviation.

Answer:

ii. Both the means are same.

iii. Scores of English are more scattered than scores of Mathematics, since standard deviation of English is 13.03 and that of Mathematics is 7.20.

Question 4.

In a school kalotsva 10 students participated in English recitation competition. The scores obtained by them are given below:

13,15,16,15,18,15,14,18,17,10

i. Find the mean score.

ii. Find the mean deviation about the mean.

Answer:

Question 5.

Find variance and standard deviation for the following data:

Answer:

Question 6.

Given below the number of telephone calls received at an exchange for 245 days:

i. Calculate the median.

ii. Calculate mean deviation about the median.

Answer:

Question 7.

a. Mean and SD of the following set of observations 1,2,3,4,’5,6 is

a.

b. 3,3

c.

d.

b. 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.

Answer:

**Long Answer** **Type Questions **

**(Score 6)**

Question 1.

a. Ifthe mean deviations about the median of the numbers a, 2a,…….. 50 a is 50, then |a| equal to

a. 3

b. 4

c. 5

d.2

b. Find mean deviation from the mean for the observations -1,0,4.

Answer:

a. 4

Numbers are a, 2a, 3a, …………..50a

total numbers = 50

hence value of n is even

Question 2.

i. The value of arithmetic mean of differences of a finite number of observations from their arithmetic mean is

ii.Find the mean of the first n odd natural numbers.

Answer:

Question 3.

i. Find the mean deviation from median of 32,37,30,41,34,39,43,33,35

ii. The mean and standard deviation of 10 observations is found to be 10 and 4 respectively. Later it was found that one item is mistaken as 10 instead of 12. Find the correct mean and standard deviation.

Answer:

Question 4.

Consider the following data:

6,8,10,12,14,16,20,22,24

i. Find its mean.

ii. Find its mean deviation about mean.

iii. Find its variance and standard deviation. Also find the coefficient of variation of the data.

Answer:

Question 5.

for the frequency :

find:

a. Mean

b. Variance.

Answer:

Question 6.

The scores of two batsman A and B in 5 inning during a certain match are as follows.

Find

a. Mean score of each batsman

b. Standard deviation of the scores of each batsman.

c. Which of the batsman is more consistent

Answer:

A | B | ||

X | X^{2} | X | X^{2} |

10 | 100 | 8 | 64 |

15 | 225 | 9 | 81 |

80 | 6400 | 7 | 49 |

70 | 4900 | 10 | 100 |

25 | 625 | 6 | 36 |

200 | 12250 | 40 | 330 |

Question 7.

Consider the numbers 4,7,8,9,10,12,13,17.

i. Find the mean of the number

ii. Find the mean deviation about the mean.

iii. Find the standard deviation.

Answer:

**NCERT Questions and Answers**

Question 1.

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

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

Answer:

Mean of the given data is,

The deviations of the respective observations from the mean , i.e., x- are

6-9,7-9,10-9,12-9,13-9,4-9,8-9,12 -9

or-3,-2,1,3,4,-5,-1,3

The absolute values of the deviations, i.e.,

|x- | are 3,2,1,3,4,5,1,3

The required mean deviation about the mean,

Question 2.

Find the mean deviation from the median for the following data:

3, 9, 5,3,12.10,18,4,7,19,21

Answer:

Here median = M.D(M)=

25.

Given the following table:

Find the mean derivation from the mean

Answer:

Question 3.

For the frequency table:

Calculate mean deviation from the median.

Answer:

The given observations are already in ascending order. Adding a row corresponding to cumulative frequencies to the given data, we get

Now, N = 30 which is even.

Median is the mean of the 15^{th} and 16^{th }observations. Both of these observations in the cumulative frequency 18, for which the corresponding observation is 13.

Therefore, Median,

Now, absolute values of the deviations from median i.e., |x_{1}– M| are shown in table.

Question 4.

Find mean deviation from mean for the following table:

Answer:

Question 5.

The scores of a batsman in 10 matches are as follows:

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

i. Find the arithmetic mean of the scores.

ii. Calculate the variance.

iii. Also find standard deviation.

Answer:

Question 6.

Find mean deviation about median:

Answer:

Question 7.

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

Answer:

The variance of the distribution of wages in plant A( σ_{1}^{2}) = 81

Therefore, standard deviation of the distribution of wages in plant A (σ_{1}) = 9 Also, the variance of the distribution of wages in plant B (σ_{2}^{2}) = 100 Therefore, standard deviation of the distribution of wages in plant B (σ_{2}) = 10

Since the average monthly wages in both the plants is same, i.e., Rs.2500, therefore, the plant with greater standard deviation will have more variability.

Thus, the plant B has greater variability in the individual wages.

Question 8.

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

Answer:

Question 9.

From the data given below state which group is more variable/which group is more consistent?

Answer:

Question 10.

The variance of 20 observations is 5. If each obsevation is multiplied by 2, find the new variance of the resulting observations.

Answer:

Question 11.

The mean of 5 observations is 4.4 and their variance is 8.24. If three of the observations are 1,2 and 6, And the other two observations.

Answer:

Let the remaining two observations be x and y. Then

Question 12.

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.

i. If the wrong item is omitted.

ii. If it is replaced by 12.

Answer: