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## Tamilnadu Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions

Exercise 8.1

Question 1.

The following data gives the number of residents in an area based on their age. Find the average age of the residents.

Solution:

Question 2.

Find the mean for the following frequency table :

Solution:

Let Assumed mean A = 170

Question 3.

Find the mean for the following distribution using step Deviation Method.

Solution:

Let Assumed mean A = 28, Class width C = 8

Exercise 8.2

Question 1.

For the following up grouped data 8, 15, 14, 19, 11, 16, 10, 8, 17, 20. Find the median.

Solution:

Arrange the values in ascending order 8, 8, 10, 11, 14, 15, 16, 17, 19, 20

The number of values = 10

Question 2.

The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.

Solution:

Question 3.

The median of the following data is 24. Find the value of x.

Solution:

Question 4.

The following are the scores obtained by 11 players in a cricket match 7, 21, 45, 12, 56, 35, 25, 0, 58, 66, 29. Find the median score.

Solution:

Let us arrange the values in ascending order 0, 7, 12, 21, 25, 29, 35, 45, 56, 58, 66

The number of values = 11 which is odd.

Exercise 8.3

Question 1.

Find the mode of the given data : 65, 65, 71, 71, 72, 75, 82, 72, 47, 72.

Solution:

In the given data 72 occurs thrice. Hence the mode is 72.

Question 2.

Find the mode:

Solution:

7 has the maximum frequency 21. Therefore 7 is the mode.

Question 3.

Find the mode for the following data.

Solution:

Question 4.

In a distribution, the mean and mode are 46 and 40 respectively. Calculate the median.

Solution:

Given, Mean = 46 and mode = 40

Using mode ≈ 3 median – 2 mean ,

40 ≈ 3 Median – 2 (46)

3 Median ≈ 40 + 92

Therefore, Median ≈ \(\frac{132}{3}\) = 44

Exercise 8.4

Multiple Choice Questions :

Question 1.

The mean of first 10 natural numbers.

(1) 25

(2) 55

(3) 5.5

(4) 2.5

Solution:

(3) 5.5

Question 2.

The mean of a distribution is 23, the median is 24 and the mode is 25.5. It is most likely that this distribution is :

(1) Positively skewed

(2) Symmetrical

(3) Asymptotic

(4) Negatively skewed

Hint: For Negatively skewed means is likely to be less than mode and median

Solution:

(4) Negatively skewed

Question 3.

The middle value of an ordered array of numbers is the

(1) Mode

(2) Mean

(3) Median

(4) Mid point

Solution:

(3) Median

Question 4.

The weights of students in a school is a :

(1) Discrete variable

(2) Continuous variable

(3) Qualitative variable

(4) None of these

Solution:

(2) Continuous variable

Question 5.

The first hand and unorganized form data is called

(1) Secondary data

(2) Organised data

(3) Primary data

(4) None of these

Solution:

(3) Primary data