Measures of Central Tendency
ICSE · Class 10 · Mathematics
Flashcards for Measures of Central Tendency — ICSE Class 10 Mathematics. Quick Q&A cards covering key concepts, definitions, and formulas.
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Get startedSolve the mean of these observations: 4, 6, 8, 10
Answer
Step 1: Add all observations: 4 + 6 + 8 + 10 = 28. Step 2: Count the observations: 4. Step 3: Divide sum by number of observations: 28/4 = 7. Answer: Mean = 7.
Solve the mean of these observations: 12, 15, 18, 21, 24
Answer
Step 1: Add the values: 12 + 15 + 18 + 21 + 24 = 90. Step 2: Count the observations: 5. Step 3: Mean = 90/5 = 18. Answer: Mean = 18.
Why is the mean written as sum of observations divided by number of observations?
Answer
Mean is the balance point of the data values. If all values are shared equally among the observations, each observation gets the same share. Formula: x̄ = (x1 + x2 + x3 + ... + xn)/n = Σxi/n. Quick ch…
Formula for mean by direct method for grouped data
Answer
Formula: Mean = Σfx / Σf. Here, f = frequency and x = value. Quick example: If x = 2, 4 and f = 3, 2, then Σfx = 2×3 + 4×2 = 14 and Σf = 5. Mean = 14/5 = 2.8.
Use the direct method to find the mean for x = 5, 10, 15 with frequencies 2, 3, 1
Answer
Step 1: Multiply each value by its frequency. 5×2 = 10, 10×3 = 30, 15×1 = 15. Step 2: Add fx values: 10 + 30 + 15 = 55. Step 3: Add frequencies: 2 + 3 + 1 = 6. Step 4: Mean = Σfx / Σf = 55/6. Answer: …
When do you use the short-cut method for mean?
Answer
The short-cut method is used when calculations can be made easier by choosing an assumed mean A. Formula: Mean = A + Σfd / Σf, where d = x - A. Example: If A = 10, x values are 8, 10, 12 with frequenc…
Use the short-cut method for mean: x = 8, 10, 12 and f = 2, 3, 1, taking A = 10
Answer
Step 1: Find d = x - A. For 8, d = -2; for 10, d = 0; for 12, d = 2. Step 2: Find fd. 2×(-2) = -4, 3×0 = 0, 1×2 = 2. Step 3: Add Σfd = -4 + 0 + 2 = -2. Step 4: Add Σf = 2 + 3 + 1 = 6. Step 5: Mean = A…
Why does the assumed mean method make calculation easier?
Answer
The assumed mean method reduces large numbers into smaller deviations. Instead of multiplying big values directly, deviations from a nearby value are used. Example: For values 48, 50, 52, choosing A =…
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