Median of grouped data

1. Find total frequency N. 2. Compute N/2. 3. Locate the median class using cumulative frequency. 4. Note l, cf, f, and h. 5. Substitute into the median formula.

Use a cumulative frequency table to mark N/2 and identify the median class clearly.

A common wrong answer is to use the modal class or the largest frequency class instead of the median class.

The median of grouped data is the middle value that divides the frequency distribution into two equal parts.

The median of grouped data is the middle value that divides the frequency distribution into two equal parts. Median = l + [(N/2 - cf) / f] x h, where l is lower boundary, cf is cumulative frequency before median class, f is frequency of median class, and h is class width. If the total frequency is 50, the median is located around the 25th observation and then calculated using the median class.

For grouped data, we first find the median class using cumulative frequency. Then we apply the median formula with lower boundary, total frequency, cumulative frequency before the median class, and class width. This gives the central value of the distribution. Median = l + [(N/2 - cf) / f] x h, where l is lower boundary, cf is cumulative frequency before median class, f is frequency of median class, and h is class width. If N = 40, N/2 = 20. Suppose cumulative frequencies are 5, 13, 22, 30. The median class is the class where cumulative frequency first crosses 20, that is the third class. If l = 20, cf = 13, f = 9, and h = 10, then median = 20 + [(20 - 13)/9] x 10 = 27.78. Questions usually give grouped data and ask for the median using cumulative frequency and the standard median formula. A common wrong answer is to use the modal class or the largest frequency class instead of the median class.