Median of Grouped Data Worksheet

Median of Grouped Data

Read each question carefully and provide your answers in the space provided. Show all your work for calculations.

When data is presented in a frequency distribution table, we can estimate the median using a specific formula. Recall that the median is the middle value of a dataset when it is ordered. For grouped data, we first identify the median class, then use the formula:

Median = L + [((N/2) - C) / f] * h

Where:

L = Lower boundary of the median class

N = Total frequency

C = Cumulative frequency of the class preceding the median class

f = Frequency of the median class

h = Class width

1. Explain in your own words why we use a formula to estimate the median for grouped data, rather than finding the exact middle value.

2. For the formula Median = L + [((N/2) - C) / f] * h, the term N/2 represents the  , and 'h' represents the  .

3. The following table shows the distribution of scores of 50 students in a math test:

Calculate the median score for this data.

4. In a grouped frequency distribution, if the cumulative frequency of the class preceding the median class is 25, and the (N/2)th item is 30, what does this imply?

5. Consider the following frequency distribution of daily wages of 100 workers:

Determine the median daily wage.

6. The median for grouped data can sometimes be equal to the upper boundary of the median class.

7. Describe a scenario where calculating the median of grouped data would be more appropriate than calculating the mean.