Jharkhand Board JAC Class 9 Maths Important Questions Chapter 14 Statistics Important Questions and Answers.

## JAC Board Class 9th Maths Important Questions Chapter 14 Statistics

Question 1.

The marks obtained by 40 students of class IX in a mathematics test are given below:

18, 55, 68, 79, 85, 43, 29, 68, 54, 73, 47, 35, 72, 64, 95, 44, 50, 77, 64, 35, 79, 52, 45, 54, 70, 83, 62, 64, 72, 92, 84, 76, 63, 43, 54, 38, 73, 68, 52, 54.

Prepare a frequency distribution table with class size of 10 marks.

Solution :

Question 2.

Below are the marks obtained by 30 students of a class in Maths test out of 100. Make a frequency distribution table for this data with class interval of size 10 and draw a histogram to represent the data. 55, 61, 46, 100, 75, 90, 77, 60, 48, 58, 64, 59, 60, 78, 55, 88, 60, 37, 58, 84, 62, 44, 52, 50, 56, 95, 67, 70, 39, 68.

Solution :

Marks obtained by 30 students are 55, 61, 46, 100, 75, 90, 77, 60, 48, 58, 64, 59, 60, 78, 55, 88, 60, 37, 58, 84, 62, 44, 52, 50, 56, 95, 67, 70, 39, 68.

Question 3.

Find the mean of the factors of 24.

Solution :

Various factors of 24 = 1, 2, 3, 4, 6, 8, 12 and 24.

Mean,

\(\bar{x}\) = Sum of all observations / Total number of observations

= \(\frac{1+2+3+4+6+8+12+24}{8}\)

= \(\frac{60}{8}=\frac{15}{2}\) = 7.5

Question 4.

Find the range of the given data: 25.7, 16.3, 2.8, 21.7, 24.3, 22.7 and 24.9

Solution :

Range of the data = Highest value – Lowest value = 25.7 – 2.8 = 22.9

Multiple Choice Questions

Question 1.

The median of following series 520, 20, 340, 190, 35, 800, 1210, 50, 80 is

(a) 1210

(b) 520

(c) 190

(d) 35

Solution :

(c) 190

Question 2.

If the arithmetic mean of 5, 7, 9, x is 9 then the value of x is

(a) 11

(b) 15

(c) 18

(d) 16

Solution :

(b) 15

Question 3.

The mode of the distribution 3, 5, 7, 4, 2, 1, 4, 3, 4 is

(a) 7

(b) 4

(c) 3

(d) 1

Solution :

(b) 4

Question 4.

If the mean and median of a set of numbers are 8.9 and 9 respectively, then the mode will be

(a) 7.2

(b) 8.2

(c) 9.2

(d) 10.2

Solution :

(c) 9.2

Question 5.

A student got marks in 5 subjects in a monthly test is given below: 2, 3, 4, 5, 6. In these obtained marks, 4 is the

(a) Mean and median

(b) Median but no mean

(c) Mean but no median

(d) Mode

Solution :

(a) Mean and median

Question 6.

Find the mode from the following table:

Marks obtained | 3 | 1 | 23 | 33 | 43 |

Frequency (f) | 7 | 11 | 15 | 8 | 3 |

(a) 13

(b) 43

(c) 33

(d) 23

Solution :

(d) 23

Question 7.

If the class intervals in a frequency distribution are (72 – 73.9), (74 – 75.9), (76 – 77.9), (78 – 79.9) etc., the mid-point of the class (74 – 75.9) is

(a) 74.50

(b) 74.90

(c) 74.95

(d) 75.00

Solution :

(c) 74.95

Question 8.

Which one of the following is not correct –

(a) Statistics is liable to be misused.

(b) The data collected by the investigator to be used by himself are called primary data.

(c) Statistical laws are exact.

(d) Statistics do not take into account of individual cases.

Solution :

(c) Statistical laws are exact.

Question 9.

If the first five elements of a sequence are replaced by (x_{i} + 5), where i = 1, 2, 3, … 5 and the next five elements are replaced by (x_{i} – 5), where, i = 6; ….. 10 then the mean will change by

(a) 25

(b) 10

(c) 5

(d) 0

Solution :

(d) 0

Question 10.

The following numbers are given: 61, 62, 63, 61, 63, 64, 64, 60, 65, 63, 64, 65, 66, 64. The difference between their median and mean is

(a) 0.4

(b) 0.3

(c) 0.2

(d) 0.1

Solution :

(b) 0.3

Question 11.

The value of \(\sum_{i=i}^n\) (x_{i} – \(\bar{x}\)) where \(\bar{x}\) is the arithmetic mean of x_{i} is

(a) 1

(b) n x

(c) 0

(d) None of these

Solution :

(c) 0

Question 12.

The average of 15 numbers is 18. The average of first 8 is 19 and that of last 8 is 17, then the 8th number is

(a) 15

(b) 16

(c) 18

(d) 20

Solution :

(c) 18

Question 13.

In an examination, 10 students scored the following marks in Mathematics: 35, 19, 28, 32, 63, 02, 47, 31, 13, 98. Its range is

(a) 96

(b) 02

(c) 98

(d) 50

Direction: questions 14 is based on the histogram given in the adjacent figure.

Solution :

(a) 96

Question 14.

The percentage of students in science faculty in 1990-91 is:

(a) 26.9 %

(b) 27.8 %

(c) 14.81 %

(d) 30.2 %

Solution :

(c) 14.81 %

Question 15.

For the scores 8, 6, 10, 12, 1, 5, 6 and 6, the arithmetic mean is

(a) 6.85

(b) 6.75

(c) 6.95

(d) 7

Direction: Each question from 16 to 18 is based on the histogram given in the adjacent figure.

Solution :

(b) 6.75

Question 16.

What is the number of workers earning ₹ 300 to 350?

(a) 50

(b) 40

(c) 45

(d) 130

Solution :

(a) 50

Question 17.

In which class interval of wages there is the least number of workers?

(a) 400 – 450

(b) 350 – 400

(c) 250 – 300

(d) 200 – 250

Solution :

(d) 200 – 250

Question 18.

What is the upper limit of the class interval 200-250?

(a) 200

(b) 250

(c) 225

(d) None of these

Solution :

(b) 250