Question
For the data set: 4, 7, 2, 9, 4, 6, 4, 8, 3 — calculate the mean, median, and mode.
Solution — Step by Step
Unordered: 4, 7, 2, 9, 4, 6, 4, 8, 3
Ordered: 2, 3, 4, 4, 4, 6, 7, 8, 9
There are 9 data points. Always arrange data before finding median.
For 9 data points (odd number), the median is the value in the ordered set.
Ordered set: 2, 3, 4, 4, 4, 6, 7, 8, 9
The 5th value is 4.
Count the frequency of each value:
| Value | Frequency |
|---|---|
| 2 | 1 |
| 3 | 1 |
| 4 | 3 |
| 6 | 1 |
| 7 | 1 |
| 8 | 1 |
| 9 | 1 |
The value 4 appears 3 times — more than any other value.
Why This Works
Mean measures the “balancing point” of the data — it accounts for every value.
Median measures the “middle” when data is ordered — it is resistant to extreme values (outliers). If we replaced 9 with 900, the median would still be 4, but the mean would shoot up.
Mode identifies the most common value — useful for categorical data or when you want to know what’s “typical” in a frequency sense.
In this dataset, all three give similar values (mean ≈ 5.22, median = 4, mode = 4), indicating a fairly symmetric distribution skewed slightly upward by the value 9.
Alternative Method — Shortcut for Mean
Instead of adding all 9 numbers, note that three 4s appear. Reorganise:
, then add . Total = . Mean = .
Common Mistake
The most common error for median: not arranging the data first. Many students find the 5th value in the unordered list (which would be 4 in this case — lucky coincidence!) instead of the ordered list. For data like 2, 9, 1, 7, 3, the unordered 5th value (3) would be wrong; the median is 3 only after ordering: 1, 2, 3, 7, 9. Always sort first.
For an even number of data points: median = average of the two middle values. For 8 data points, the median = average of the 4th and 5th values. For odd number of data points (like this problem with 9): median = single middle value at position .