Measures Of Central Tendency
ICSE · Class 11 · Economics
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Quick Quiz: Measures Of Central Tendency
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A series has five values: 20, 30, 40, 50, and 60. What is the arithmetic mean of the series?
A worker’s daily wages are 1000, 1200, 1400, 1600, 1800, 2000, and 2200 rupees. Find the arithmetic mean wage.
Two groups have 30 items with mean 42 and 20 items with mean 35. What is the combined mean?
Three groups have sizes 20, 30, and 50 with means 40, 35, and 30. What is the combined mean?
Sample Questions
A mean of 48 was calculated for 100 observations. Later, one value was found to be 73 instead of 53. What is the correct mean?
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47.8
Original sum = 100 × 48 = 4800. Correct sum = 4800 - 73 + 53 = 4780. Correct mean = 4780/100 = 47.8.
A weighted mean is needed for values 10, 20, 30, 40 with weights 1, 2, 3, 4. What is the weighted arithmetic mean?
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30
Compute ΣWX = 10×1 + 20×2 + 30×3 + 40×4 = 10 + 40 + 90 + 160 = 300. Compute ΣW = 1 + 2 + 3 + 4 = 10. Weighted mean = 300/10 = 30.
A continuous series has frequencies 8, 15, 25, 32, 15, 5 in class intervals 0-10, 10-20, 20-30, 30-40, 40-50, 50-60. What is the median?
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30.625
Total frequency N = 100, so median position is N/2 = 50th item. Cumulative frequencies are 8, 23, 48, 80, 95, 100, so the median class is 30-40. Use M = L1 + (i/f)(m-c) = 30 + (10/32)(50-48) = 30 + 0.625 = 30.625.
A continuous series in descending order has median class 30-40, upper limit 40, class interval 10, frequency 32, median position 50, and preceding cumulative frequency 20. What is the median?
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30.625
For descending order, use M = L2 - (i/f)(m-c). Substitute values: M = 40 - (10/32)(50-20) = 40 - 9.375 = 30.625.
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