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Q.

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: 

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:

(i) Draw a histogram to depict the given information. 

(ii) Write the class interval in which the maximum number of surnames lie.

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Detailed Solution

(i) Histogram of the given data, 

A random sample of 100 surnames was taken from a local phone book, and the frequency distribution of the letters in the English alphabet was found to be as follows:

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

On the x-axis, we'll plot the total number of letters, and on the y-axis, the percentage of surnames that occur every two letters.

For the y-axis, we will select a suitable scale of 1 unit Equals 4 surnames.

here classes are continued so we draw the histogram easily

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:

(ii) Write the class interval in which the maximum number of surnames lie:

The  class interval in which the maximum number of surnames lie is 6 - 8.

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