The Median for grouped data

Recall that the median is different for odd and for even numbers of observations when the data are not in the grouped form. However, if the n data are written in grouped form, then median is simply defined as the observation.

Thus, if we have the frequency distribution of 100 observations, then the observation in order of size would be the median; if we have 101 observations then the observation would be the median.

To find median, first, we need to find the class which contains the middle observation. Let M denotes the number of this class, where M is the some integers from 1 to k. If the median occurs in the fifth class then M =5; if it occurs in the seventh class, then M =7; and so on.

Let the frequency of the class be denoted by . Next, note how many observations are in classes preceding the median class; denote this cumulative frequency by .

The general formula for median is

where

lower boundary of the median class

number of observations

the number of observations in the median class

the number of observations in the classes

preceding the median class

width of the median class

Example: Find the median of the frequency distribution

Starting monthly salary(in dollars)	Frequency
900-1000 1000-1100 1100-1200 1200-1300 1300-1400 1400-1500 1500-1600
	n =12

Solution:

First of all, let us divide n (the number of all observations) to find the halfway point.

To find the class that contains observation it is necessary to form cumulative frequency distribution. This class is called the median class; it contains the median:

Starting monthly salary(in dollars)	Frequency	Cumulative frequency
900-1000 1000-1100 1100-1200 1200-1300 1300-1400 1400-1500 1500-1600

observation is in class. So, the median class is 1000-1100.

Now let us apply

In our case

; ; ;

After substituting we get

The median is 1100. In other words, median as a measure of center indicates that average value of monthly salaries of 12 employees is 1100$.

Дата добавления: 2015-08-05