Using empirical formula, calculate the mode for the following data. 17, 20, 21, 18, 25, 28, 24, 22, 16, 24, 25, 24
25
Mode using the Empirical Formula
Given the data set:
17, 20, 21, 18, 25, 28, 24, 22, 16, 24, 25, 24
Step 1 — Sort the data
Sorted ascending:
16, 17, 18, 20, 21, 22, 24, 24, 24, 25, 25, 28
Step 2 — Mean
Sum = 264, N = 12 → Mean = 264 / 12 = 22
Step 3 — Median
Even number of items (12). Median = average of 6th and 7th values = (22 + 24)/2 = 23
Step 4 — Apply empirical formula
The empirical relation is:
Mode = 3 × Median − 2 × Mean
Mode = 3 × 23 − 2 × 22 = 69 − 44 = 25
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