Example 1 · level 1
Marks of 5 students in a mock test: 85, 90, 44, 91, 38. Find the arithmetic mean (two decimals if needed).
Show solution
- Σx = 85 + 90 + 44 + 91 + 38 = 348.
- Mean = 348 ÷ 5 = 69.6.
Answer: 69.6
CA FOUNDATION: QUANTITATIVE APTITUDE · MEASURES OF CENTRAL TENDENCY AND DISPERSION
Mean, median and mode
Mean = Σx ÷ n. Median = middle value after sorting. Empirical relation: Mode = 3 Median − 2 Mean.
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Worked examples
Example 2 · level 2
Find the median of these weekly sales figures (units): 53, 56, 58, 61, 23, 34, 42.
Show solution
- Sorted: 23, 34, 42, 53, 56, 58, 61.
- Middle (4th) value = 53.
Answer: 53
Example 3 · level 3
In a moderately skewed distribution of daily sales (₹ thousand) at Sharma Traders, mean = 80.5 and median = 83.5. Estimate the mode.
Show solution
- Mode = 3 × 83.5 − 2 × 80.5
- = 250.5 − 161 = 89.5.
Answer: 89.5