Calculation of Median for Given Data Set

The median is the central value of a data set, which means that half of the values in the data set are above it and half are below it. To calculate the median for the given data set, follow these steps:

Step 1: Arrange Data in Ascending Order

The first step in calculating the median is to arrange the data set in ascending order. The given data set is already arranged in ascending order as follows:

Mid Value: 5, 15, 25, 35, 45, 55, 65, 75

Frequency: 15, 7, 11, 10, 13, 8, 20, 16

Step 2: Find the Cumulative Frequency

The next step is to find the cumulative frequency for each mid-value. Cumulative frequency is the sum of the frequency of a mid-value and the frequencies of all the mid-values that come before it. The cumulative frequency for the given data set is as follows:

Mid Value: 5, 15, 25, 35, 45, 55, 65, 75

Frequency: 15, 7, 11, 10, 13, 8, 20, 16

Cumulative Frequency: 15, 22, 33, 43, 56, 64, 84, 100

Step 3: Calculate the Median

The median is calculated by finding the mid-value where the cumulative frequency is equal to half of the total frequency. The total frequency for the given data set is 100. Half of the total frequency is 50.

To find the median, we need to find the mid-value where the cumulative frequency is equal to or greater than 50. From the cumulative frequency table, we can see that the mid-value where the cumulative frequency is equal to or greater than 50 is 45.

Therefore, the median for the given data set is 45.

Conclusion

In conclusion, the median for the given data set is 45. The median is a useful measure of central tendency that can be used to describe the typical value of a data set. By following the steps above, you can easily calculate the median for any given data set.