RS Aggarwal - Mathematics

Book: RS Aggarwal - Mathematics

Chapter: 30. Statistics

Subject: Maths - Class 11th

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Chapter Exercises

Exercise 30A
Exercise 30B
Exercise 30C
Exercise 30D

Exercise 30A

1

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

7, 8, 4, 13, 9, 5, 16, 18
2

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

39, 72, 48, 41, 43, 55, 60, 45, 54, 43
3

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

17, 20, 12, 13, 15, 16, 12, 18, 15, 19, 12, 11
4

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

12, 5, 14, 6, 11, 13, 17, 8, 10
5

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

4, 15, 9, 7, 19, 13, 6, 21, 8, 25, 11
6

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

34, 23, 46, 37, 40, 28, 32, 50, 35, 44
7

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

70, 34, 42, 78, 65, 45, 54, 48, 67, 50, 56, 63
8

Find the mean deviation about the mean for the following data :
9

Find the mean deviation about the mean for the following data :
10

Find the mean deviation about the mean for the following data :
11

Find the mean deviation about the median for the following data :
12

Find the mean deviation about the median for the following data :
13

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


Xi



10



15



20



25



30



35



40



45



Fi



7



3



8



5



6



8



4



9
14

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


Mark



0-10



10-20



20-30



30-40



40-50



50-60



Number of Students



6



8



14



16



4



2
15

Find the mean deviation about the mean for the following data :
16

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


class



30-40



40-50



50-60



60-70



70-80



80-90



90-100



Frequency



3



7



12



15



8



3



2
17

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


class



0-10



10-20



20-30



30-40



40-50



50-60



Frequency



6



7



15



16



4



2
18

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


class



0-10



10-20



20-30



30-40



40-50



50-60



Frequency



6



8



11



18



5



2

Exercise 30B

1

Find the mean, variance and standard deviation for the numbers 4, 6, 10, 12, 7, 8, 13, 12.
2

Find the mean, variance and standard deviation for the first six odd natural numbers.
3

Using short cut method, find the mean, variation and standard deviation for the data :


xi



4



8



11



17



20



24



32



fi



3



5



9



5



4



3



1
4

Using short cut method, find the mean, variation and standard deviation for the data :
5

Using short cut method, find the mean, variation and standard deviation for the data :
6

Using short cut method, find the mean, variation and standard deviation for the data :
7

Using short cut method, find the mean, variation and standard deviation for the data :
8

Using short cut method, find the mean, variation and standard deviation for the data :


Class



30-40



40-50



50-60



60-70



70-80



80-90



90-100



Frequency



3



7



12



15



8



3



2
9

Using short cut method, find the mean, variation and standard deviation for the data :

Exercise 30C

1

If the standard deviation of the numbers 2, 3, 2x, 11 is 3.5, calculate the possible values of x.
2

The variance of 15 observations is 6. If each observation is increased by 8, find the variance of the resulting observations.
3

The variance of 20 observations is 5. If each observation is multiplied by 2. Find the variance of the resulting observations.
4

The mean and variance of five observations are 6 and 4 respectively. If three of these are 5, 7 and 9, find the other two observations.
5

The mean and variance of five observations are 4.4 and 8.24 respectively. If three of these are 1, 2 and 6, find the other two observations.
6

The mean and standard deviation of 18 observations are found to be 7 and 4 respectively. On rechecking it was found that an observation 12 was misread as 21. Calculate the correct mean and standard deviation.
7

For a group of 200 candidates, the mean and standard deviations of scores were found to be 40 and 15 respectively. Later on it was discovered that the score of 43 was misread as 34. Find the correct mean and standard deviation.
8

The mean and standard deviations of a group of 100 observations were found to be 20 and 3 respectively. Later on it was found that three observations 21, 12 and 18 were incorrect. Find the mean and standard deviation if the incorrect observations were omitted.

Exercise 30D

1

The following results show the number of workers and the wages paid to them in two factories F1 and F2.

Which factory has more variation in wages?
2

Coefficient of variation of the two distributions are 60% and 80% respectively, and their standard deviations are 21 and 16 respectively. Find their arithmetic means.
3

The mean and variance of the heights and weights of the students of a class are given below:


Heights



Weights



Mean



63.2 inches



63.2 kg



SD



11.5 inches



5.6 kg



Which shows more variability, heights or weights?
4

The following results show the number of workers and the wages paid to them in two factories A and B of the same industry.

(i) Which firm pays a larger amount as monthly wages?


(ii) Which firm shows greater variability in individual wages?
5

The sum and the sum of squares of length x (in cm) and weight y (in g) of 50 plant products are given below:


Which is more variable, the length or weight?