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 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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