# How to calculate the estimated mean and estimated median of grouped data?

In this tutorial, we will try to learn the followings;

1. Estimated mean
2. Estimated median
3. Estimated mode
4. Class intervals
 Age Mid  of age Frequency Mid * Frequency 21 – 25 23 5 23 * 5 =  115 26 – 30 28 2 28 * 2 = 56 31 – 35 33 6 33 * 6 = 198 35 – 40 37 8 37 * 8 = 296 Total 21 665

Estimated Mean = 665 / 21

= 31.66

Class intervals:

Group 21 to 25, 26 to 30, 31 to 35 and 35 to 40 are class intervals.

Mean is 31.6 so 31.6 rounds to 32.

Estimated mean =  32

Median group = 31 to 35

Estimated Median = ?

Estimated Median = L + (TV / 2) – SBM  ⁄  FMG  * GW

 L = Lower boundary of median group 30.5 TV =  Total number of values 21 SBM = Sum of frequencies before median group 7 FMG = Frequency of median group 6 GW = Group width 5

Result: Our median group is 31 to 35 and yes estimated median 33.4 is in the median group.

How to calculate the estimated mode of the above-grouped data?

 L = Lower boundary of the median group 30.5 SBM = sum of frequencies before the median group 7 FMG = Frequency of median group 6 FBMG = Sum of frequencies of all groups before the median group 7 FBMG = Sum of frequencies of all groups after median group 8 GW = Group width 5

Mode: Mode is the most occurring Value in the data.