How do you determine the median in a frequency table?

To determine the median in a frequency table, find the middle value when the data is ordered.

First, you need to calculate the cumulative frequency for each class or category in the table. The cumulative frequency is the running total of the frequencies up to and including the current class. This helps you see how the data accumulates across the different classes.

Next, identify the total number of data points, which is the sum of all the frequencies in the table. If the total number of data points (n) is odd, the median is the value at the \((n+1)/2\)th position. If \(n\) is even, the median is the average of the values at the \(n/2\)th and \((n/2 + 1)\)th positions.

To find the median class, look at the cumulative frequencies and locate the class interval that contains the median position. This is the class where the cumulative frequency first exceeds the median position.

For example, if you have a frequency table with the following data:

| Class Interval | Frequency |
|----------------|-----------|
| 1-10 | 3 |
| 11-20 | 5 |
| 21-30 | 7 |
| 31-40 | 4 |
| 41-50 | 1 |

First, calculate the cumulative frequencies:

| Class Interval | Frequency | Cumulative Frequency |
|----------------|-----------|----------------------|
| 1-10 | 3 | 3 |
| 11-20 | 5 | 8 |
| 21-30 | 7 | 15 |
| 31-40 | 4 | 19 |
| 41-50 | 1 | 20 |

The total number of data points is 20. Since 20 is even, the median position is the average of the 10th and 11th positions. The cumulative frequency shows that both the 10th and 11th positions fall within the 21-30 class interval. Therefore, the median lies within this interval.