finding the estimated mean, median and mode for grouped data in data mining

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

AgeMid  of ageFrequencyMid * Frequency
21 – 2523523 * 5 =  115
26 – 3028228 * 2 = 56 
31 – 3533633 * 6 = 198
35 – 4037837 * 8 = 296
Total 21665

Estimated Mean = 665 / 21

                             = 31.66

[quads id=1]

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 group30.5
TV =  Total number of values21
SBM = Sum of frequencies before median group7
FMG = Frequency of median group6
GW = Group width5

estimated median in grouped data in data mining

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 median group30.5
SBM = sum of frequencies before median group7
FMG = Frequency of median group6
FBMG = Sum of frequencies of all groups before median group7
FBMG = Sum of frequencies of all groups after median group8
GW = Group width5

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

[quads id=2]

estimated mode of grouped data in data mining