$\begin{array}{c|c} Age(years) & 13 & 14 & 15 & 16 & 17 \\ \hline Frequency & 10 & 24 & 8 & 5 & 3 \end{array}$ Find the median age

Analyze the question: We need the median age from a frequency table. The median is the middle value when all the ages are arranged in order.

Concept: For a frequency distribution, find the total frequency N, locate the middle position, then use the cumulative frequency to see which age covers that position.

Solution:

Total frequency: N = 10 + 24 + 8 + 5 + 3 = 50

Since N is even, the median is the average of the (N/2)th and (N/2 + 1)th values, which are the 25th and 26th values.

Cumulative frequencies:

| Age | Frequency | Cumulative frequency | |-----|-----------|----------------------| | 13 | 10 | 10 | | 14 | 24 | 34 | | 15 | 8 | 42 | | 16 | 5 | 47 | | 17 | 3 | 50 |

• Positions 1 to 10 are age 13.
• Positions 11 to 34 are age 14.

Both the 25th and 26th values fall within positions 11 to 34, so both are 14.

Median = (14 + 14) / 2 = 14

Tip: Always build the cumulative frequency column first. Then find the middle position (N/2 for even N, or (N+1)/2 for odd N) and look for the first cumulative frequency that reaches or passes it. When the middle positions sit inside one big frequency, like 24 here, the median is simply that value.