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?

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

  1. Estimated mean  
  2. Estimated median
  3. Estimated mode
  4. Class intervals
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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

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 group 30.5
SBM = sum of frequencies before median group 7
FMG = Frequency of median group 6
FBMG = Sum of frequencies of all groups before 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.

estimated mode of grouped data in data mining