Question

100 surnames were randomly picked up from a local telephone directory and a frequency distribution of the number of letters in the English alphabet in the surnames was found as follows:
number of letters number of surnames
1-4 6
4-6 30
6-8 44
8-12 16
12-20 4
1. draw a histogram to depict the given information.
2. write the class interval in which the maximum number of surnames lie​

Answer 1

Answer:

Solution:

It can be observed from the given data that it has class intervals of varying widths.

The proportion of the number of surnames per 2 letters (class interval of minimum class size for reference) can be made.

(i) The length of rectangles are calculated as below:

Number of letters

Number of surnames

Width of the class

Length of rectangle

1 – 4

6

3

(6 × 2)/3 = 4

4 – 6

30

2

(30 × 2)/2 = 30

6 – 8

44

2

(44 × 2)/2 = 44

8 – 12

16

4

(16 × 2)/4 = 8

12 – 20

4

8

(4 × 2)/8 = 1

We will take the number of letters on the x-axis and the proportion of the number of surnames per every 2 letter interval on the y-axis.

We will choose an appropriate scale of 1 unit = 4 surnames for the y-axis. The histogram can be constructed as follows: