How to calculate the estimated mean and estimated median of grouped data?
In this tutorial, we will try to learn the followings;
 Estimated mean
 Estimated median
 Estimated mode
 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 abovegrouped 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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