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.

Video Lecture

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