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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.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 1
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 2
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Question 2.
Find the mean for the following frequency table :
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 3
Solution:
Let Assumed mean A = 170
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 4

Question 3.
Find the mean for the following distribution using step Deviation Method.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 5
Solution:
Let Assumed mean A = 28, Class width C = 8
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 6

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
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 7

Question 2.
The following table gives the weekly expenditure of 200 families. Find the median of the weekly expenditure.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 8
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 9
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 10
Question 3.
The median of the following data is 24. Find the value of x.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 11
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 12
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 13

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.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 60

Exercise 8.3
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
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:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 61
Solution:
7 has the maximum frequency 21. Therefore 7 is the mode.

Question 3.
Find the mode for the following data.
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 62
Solution:
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 63

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
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
Multiple Choice Questions :

Question 1.
The mean of first 10 natural numbers.
(1) 25
(2) 55
(3) 5.5
(4) 2.5
Samacheer Kalvi 9th Maths Chapter 8 Statistics Additional Questions 71
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
Samacheer Kalvi 9th Maths Solutions Chapter 8 Statistics Additional Questions
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

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