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.
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:
(ii) The class interval in which the maximum number of surnames lie is 6 – 8.
Video Solution:
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.
NCERT Solutions for Class 9 Maths - Chapter 14 Exercise 14.3 Question 9:
Summary:
The data of 100 surnames were randomly picked up from a local telephone directory is given. We have made a Histogram to represent the data. The class interval in which the maximum number of surnames lies 6 – 8.