# FIND MEAN MEDIAN AND MODE OF THE GROUPED DATA

## About "Find mean median and mode of grouped data"

Find mean median and mode of grouped data :

Here we are going to see how to find mean median and mode of grouped data.

Mean :

Arithmetic mean (AM) is one of the measures of central tendency which can be defined as the sum of all observations divided by the number of observations.

Median :

Median is defined as the middle value of the data when the data is arranged in ascending or descending order.

Mode :

If a set of individual observations are given, then the mode is the value which occurs most often.

Let us look into some example problems to understand how to find mean, median and mode of the grouped data.

Example 1 :

Find the mean, median and mode for the following frequency table:

 x102025303755 f5121415104

Solution :

Arithmetic mean  =  ∑fx / N

 x102025303755 f5121415104N  =  60 fx50240350450370220∑fx  =  1680

Arithmetic mean  =  ∑fx / N  =  1680 / 60

=  28

Hence the required arithmetic mean for the given data is 28.

Median :

 x102025303755 f5121415104 Cumulative frequency55 + 12  =  1717 + 14  =  3131 + 15  =  4646 + 10  =  5656 + 4  =  60

Here, the total frequency, N = ∑f = 60

N/2  =  60 / 2  =  30

The median is (N/2)th value = 30th value.

Now, 30th value occurs in the cumulative frequency 31, whose corresponding x value is 25.

Hence, the median = 25.

Mode :

By observing the given data set, the number 30 occurs more number of times. That is 15 times.

Hence the mode is 30.

Mean  =  28

Mode  =  25 and

Mode  =  30.

Example 2 :

Find the mean, median and mode for the following frequency table:

 x19212325272931 f13152018161713

Solution :

To find arithmetic mean for this problem, let us use assumed mean method.

Here A  =  25

 x19212325272931 f13152018161713N  =  112 d  =  x - A-6-4-20246 fd-78-60-400326878∑fd  =  0

Arithmetic mean  =  A + [∑fd / N]

=  25 + (0/112)

=  25 + 0

=  25

Hence the required arithmetic mean for the given data is 25.

Median :

 x19212325272931 f13152018161713 Cumulative frequency1313 + 15  =  2828 + 20  =  4848 + 18  =  6666 + 16  =  8282 + 17  =  9999 + 13  =  112

Here, the total frequency, N = ∑f = 112

N/2  =  112 / 2  =  61

The median is (N/2)th value = 61th value.

Now, 61th value occurs in the cumulative frequency 25, whose corresponding x value is 25.

Hence, the median = 25.

Mode :

By observing the given data set, the number 23 occurs more number of times. That is 20 times.

Hence the mode is 23.

Mean  =  25

Mode  =  25

Mode  =  23. Apart from the stuff given on this web page, if you need any other stuff in math, please use our google custom search here.

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