**Chapter 3 Data Handling**

### Very Short Answer Type

Question 1.

Find the range of the following data:

21, 16, 30, 15, 16, 18, 10, 24, 26, 20

Solution:

Greatest number 30

Smallest number = 10

Range = 30 – 10 = 20

Question 2.

Find the mode of the following data:

24, 26, 23, 26, 22, 25, 26, 28

Solution:

Arranging the given data with the same value together, we get

22, 23, 24, 25, 26, 26, 26, 28

Here, 26 occurs the greatest number of times i.e. 3 times

Thus, the required mode = 26.

Question 3.

Find the average of the numbers 8, 13, 15.

Solution:

Question 5.

Find the median of the following data:

20, 14, 6, 25, 18, 13, 19, 10, 9, 12

Solution:

Arranging the given data in increasing order, we get

6, 9, 10, 12, 13, 14, 18, 19, 20, 25

n = 10 (even)

Thus, the required median = 13.5

Question 6.

A fair die is rolled, find the probability of getting a prime number.

Solution:

Number on a die = 1, 2, 3, 4, 5, 6

n(S) = 6

Prime numbers = 2, 3, 5

n(E) = 3

Question 7.

If the averages of the given data 6, 10, 12, x, 16 is 14, find the value of x.

Solution:

Average of the given numbers

Thus, the required value of x is 26.

Question 8.

Find the mean of the first 5 multiples of 3.

Solution:

Five multiples of 3 are 3, 6, 9, 12 and 15

Hence, the required mean = 9.

### Short Answer Type

Question 9.

The following bar graph shows the number of books sold by a publisher during the five consecutive years. Read the bar graph and answer the following questions:

(i) About how many books were sold in 2008, 2009 and 2012 years?

(ii) In which years were 575 books were sold?

(iii) In which years were the minimum number of books sold?

Solution:

(ii) In the year of 2012, maximum number of books i.e. 575 were sold.

(iii) Minimum number of books i.e. 150 were sold in the year 2008.

Question 10.

Find the mean and median of first five prime numbers.

Solution:

First five prime numbers are: 2, 3, 5, 7 and 11

Here, n = 5

Median is the middle term, i.e., 5.

Question 11.

The marks obtained (out of 10) by 80 students in a class test are given below:

Find the mode of the above data.

Solution:

In the given frequency distribution table, we find that the observation 7 has maximum frequency, i.e., 20

Hence, the required mode = 7.

Question 12.

A bag contains 5 white and 9 red balls. One ball is drawn at random from the bag. Find the probability of getting

(a) a white ball

(b) a red ball

Solution:

Total number of balls = 5 + 9 = 14 balls

n(S) = 14

(i) Number of white ball = 5

n(E) = 5

Question 13.

A dice is tossed once. Find the probability of getting

(i) a number 5

(ii) a number greater than 5

(iii) a number less than 5

(iv) an odd number

(v) an even number

(vi) a number greater than 6

Solution:

Total number of outcomes = 6

n(S) = 6

(i) An event of getting a number 5

n(E) = 1

### Long Answer Type

Question 14.

The data given below shows the production of motorbikes in a factory for some months of two consecutive years.

Study the table given above and the answer the following questions:

(a) Draw a double bar graph using an appropriate scale to depict the above information and compare them.

(b) In which year was the total output maximum?

(c) Find the mean production for the year 2007.

(d) For which month was the difference between the production for the two years is the maximum?

(e) In which month for the year 2008, the production was the maximum?

(f) In which month for the year 2007, the production was the least? [NCERT Exemplar]

Solution:

(a) Double bar graph

Scale : 1 cm = 100 Motor Bikes

The above bar graph depicts the total production of motorbikes in two consecutive years.

Total production in 2007 was 22100 whereas in 2008 it was 21100.

(b) In the year 2007, the total production was maximum (22100)

(c) Mean production in the year 2007 is

(d) Production of motorbikes in the May 2007 = 4500 and in May 2008 = 3200

Difference = 4500 – 3200 = 1300 which is the maximum

(e) In the month of August 2008, production was maximum i.e., 6000

(f) In the month of Feb. 2007 the production was least i.e., 2800.

Question 15.

A coin and a die are tossed once together. Find the total number of outcomes.

Solution:

A coin has two faces, Head (H) and Tail (T)

A die has six faces marked with numbers 1, 2, 3, 4, 5, 6

Possible outcomes are:

H1, H2, H3, H4, H5, H6, T1, T2, T3, T4, T5, T6

Total number of outcomes = 2 × 6 = 12