Median

The median is another measure of central tendency that represents the middle value of a data set. To find the median, the data set is arranged in order from lowest to highest (or highest to lowest), and then the middle value is selected. If the data set has an even number of values, then the median is the average of the two middle values.

For ungrouped data, the formula for finding the median is:

• If n is odd: Median = (n + 1) / 2 th value
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• If n is even: Median = (n / 2) th value + ((n / 2) + 1) th value) / 2
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where n represents the number of values in the data set.

Example of median for ungrouped data: Consider the following set of data: 5, 6, 3, 8, 7 First, we arrange the data set in order: 3, 5, 6, 7, 8 Since the number of values in the data set is odd (n = 5), the median is the middle value, which is 6.

For grouped data, the formula for finding the median is:

Median = L + ((n/2 - F) / f) * h

where L represents the lower limit of the median class interval, n represents the total number of values in the data set, F represents the cumulative frequency up to the median class interval, f represents the frequency of the median class interval, and h represents the height of each class interval.

Example of the median for grouped data: Consider the following frequency distribution table:

Class Interval	Frequency
0-10	5
10-20	10
20-30	15
30-40	8
40-50	2

To find the median, we first calculate the cumulative frequency of each class interval:

Class Interval	Frequency	Cumulative Frequency
0-10	5	5
10-20	10	15
20-30	15	30
30-40	8	38
40-50	2	40

The median falls in the 20-30 class interval, which has a frequency of 15. Therefore, L = 20, n = 40, F = 5, f = 15, and i = 10. Plugging these values into the formula, we get:

Median = 20 + ((20 - 5.5) / 15) * 10 = 22.67

Therefore, the median for the given frequency distribution table is 22.67