If the frequency distribution of scores is 10, 20, 30, and the cumulative frequency is 60, the median lies in which class interval?

Steps to Solve

1. Identify the median position To find the class interval where the median lies, we first need to determine the position of the median within the data set. The formula for finding the position of the median in a cumulative frequency distribution is given by: $$ \text{Median Position} = \frac{n}{2} $$ where $n$ is the total frequency. Here, we have a cumulative frequency of 60, which implies $n = 60$. Thus, $$ \text{Median Position} = \frac{60}{2} = 30 $$

2. Analyze the frequency intervals Next, we need to create a cumulative frequency table based on the given frequency distribution. The frequency distribution of scores is as follows:

• 0-10: 10
• 10-20: 20
• 20-30: 30

Calculating the cumulative frequencies:

• Cumulative frequency for 0-10: 10
• Cumulative frequency for 10-20: 10 + 20 = 30
• Cumulative frequency for 20-30: 30 + 30 = 60

3. Locate the median in the cumulative frequency table From our cumulative frequency analysis, we have:

• 0-10: 10
• 10-20: 30
• 20-30: 60

Since the median position is 30, we find that this position falls within the cumulative frequency of the class interval 10-20, which indicates that the median value lies in this interval.