Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Students can download Maths Chapter 8 Statistics Additional Questions and Answers, Notes, Samacheer Kalvi 9th Maths Guide Pdf helps you to revise the complete Tamilnadu State Board New Syllabus, helps students complete homework assignments and to score high marks in board exams.

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

I. Choose the Best Answer

Question 1.
The Arithmetic mean of all the factors of 10 is ………
(a) 4.5
(b) 5.5
(c) 10
(d) 55
Solution:
(a) 4.5

Question 2.
The mean of five numbers is 27, if one number is excluded, then mean is 25. Then the excluded number is ……..
(a) 0
(b) 15
(c) 25
(d) 35
Solution:
(d) 35

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 3.
The mean of 8 numbers is 15. If each number is multiplied by 2, then the new mean will be ……..
(a) 7.5
(b) 30
(c) 10
(d) 25
Solution:
(b) 30

Question 4.
The median of 11, 8, 4, 9, 7, 5, 2, 4, 10 is ……..
(a) 1
(b) 8
(c) 4
(d) 11
Solution:
(a) 1

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 5.
Median is …….
(a) the most frequent value
(b) the least frequent value
(c) middle most value
(d) mean of first and last values
Solution:
(c) middle most value

Question 6.
The mode of the distribution is …….
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 1
(a) 3
(b) 4
(c) 6
(d) 14
Solution:
(b) 4

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 7.
Mode is …….
(a) the middle value
(b) extreme value
(c) minimum value
(d) the most repeated value
Solution:
(d) the most repeated value

Question 8.
The mode of the data 72, 33, 44, 72, 81, 72, 15 is ……..
(a) 12
(b) 33
(c) 81
(d) 15
Solution:
(a) 12

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 9.
The Arithmetic mean of 10 number is -7. If 5 is added to every number, then the new arithmetic mean is ……..
(a) 17
(b) 12
(c) -2
(d) -7
Solution:
(c) -2

Question 10.
The Arithmetic mean of integers from -5 to 5 is ……..
(a) 25
(b) 10
(c) 3
(d) 0
Solution:
(d) 0

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

II. Answer the Following Questions

Question 1.
Find the Arithmetic mean for the following data.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 2
Solution:
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 3
Arithmetic mean (\(\bar { X }\)) = \(\frac{Σfx}{Σf}\)
= \(\frac{5540}{96}\)
= 57.7
∴ Arithmetic mean = 57.7

Question 2.
Calculate the Arithmetic mean of the following data using step deviation method.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 4
Solution:
Assumed mean = 35
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 5
Arithmetic mean (\(\bar { X }\)) = A + \(\frac{Σfd}{Σf}\) × c
= 35 + \(\frac{(-20)}{100}\) × 10
= 35 – 2
= 33
∴ Arithmetic mean = 33

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 3.
Find the median for the following data.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 6
Solution:
The given class intervals is inclusive type we convert it into exclusive type.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 7
\(\frac{N}{2}\) = \(\frac{70}{2}\)
= 35
Median class is 25.5 – 30.5
Here l = 25.5, f = 26, m = 30, c = 5
Median = l + \(\frac{\frac{N}{2}-m}{f}\) × c
= 25.5 + \(\frac{35-30}{26}\) × 5
= 25.5 + \(\frac{5×5}{26}\)
= 25.5 + 0.96
= 26.46
∴ Median = 26.46

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 4.
Calculate the mode of the following data.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 8
Solution:
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 9
The highest frequency is 30. Corresponding class interval is the modal class.
Here l = 25, f = 30, f1 = 18, f2 = 20 and c = 5
Mode
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 10
∴ Arithmetic mean = 25 + 2.727
= 25 + 2.73
= 27.73
mode = 27.73

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

Question 5.
Find the mean, median and mode of marks obtained by 20 students in an examination. The marks are given below.
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 11
Solution:
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 12
Arithmetic mean:
Here Σfx = 560, Σf = 20
\(\bar { X }\) = \(\frac{Σfx}{Σf}\)
= \(\frac{560}{20}\)

Median:
Median class is 20 – 30
Here l = 20, \(\frac{N}{2}\) = 10, m = 5, c = 10, f = 5
Median
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 13
= 20 + 10
= 30

Mode:
The highest frequency is 8
Modal class is 30 – 40
Here, l = 30, f = 8, f1 = 5, f2 = 2, c = 10
Mode
Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions 14
= 33.33
Mean = 28, median = 30, mode = 33.33

Samacheer Kalvi 9th Maths Guide Chapter 8 Statistics Additional Questions

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