Question

Find the median of the following data:

Class interval 0−20 20−40 40−60 60−80 80−100 100−120 120−140
Frequency 6 8 10 12 6 5 3

Answer 1

To find the median of the frequency distribution, we compute the cumulative frequencies and determine the median class interval, which is between the 25th and 26th values. In this case, it is the 60-80 class interval.

Step-by-step explanation:

The question asks us to find the median of a given frequency distribution. Finding the median in a grouped data set involves determining the value that falls in the middle of the data set when all the observations are listed in order. Since the data provided is grouped, we cannot find the exact value of the median but we can find the class interval in which the median lies.

To find the median class interval, we need to first calculate the cumulative frequency for each class interval:

• 0−20: 6
• 20−40: 6 + 8 = 14
• 40−60: 14 + 10 = 24
• 60−80: 24 + 12 = 36
• 80−100: 36 + 6 = 42
• 100−120: 42 + 5 = 47
• 120−140: 47 + 3 = 50

The total number of observations is 50. The median will be the average of the 25th and 26th values. Since the cumulative frequency of the class 40−60 is 24 and the cumulative frequency of the class 60−80 is 36, the 25th and 26th values fall within the 60−80 class interval. This is our median class interval.