Statistics — Flashcards
ICSE · Class 11 · Mathematics
36 flashcards for Statistics (ICSE Class 11 Mathematics) to test yourself on key terms and facts. Sample: "A class has the data 6, 7, 6, 10, 12, 13, 12"
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A class has the data 6, 7, 6, 10, 12, 13, 12, 4, 8, 12. Find the arithmetic mean by the direct method.
Answer
Step 1: Add all values. 6 + 7 + 6 + 10 + 12 + 13 + 12 + 4 + 8 + 12 = 90 Step 2: Count the number of values. n = 10 Step 3: Divide total by n. Mean = 90 / 10 = 9 Answer: 9…
A data set has values 5, x, 8, y, 14 and mean 8. Find the relation between x and y.
Answer
Step 1: Use mean formula. (5 + x + 8 + y + 14) / 5 = 8 Step 2: Multiply by 5. 27 + x + y = 40 Step 3: Rearrange. x + y = 13 Answer: x + y = 13…
Find the mean of the first n natural numbers.
Answer
Step 1: Write the numbers 1, 2, 3, ..., n. Step 2: Use the direct mean formula. Mean = (1 + 2 + 3 + ... + n) / n Step 3: Use the sum formula. 1 + 2 + ... + n = n(n + 1) / 2 Step 4: Divide by n. Mean =…
Find the mean of the first n even positive integers.
Answer
Step 1: Write the numbers 2, 4, 6, ..., 2n. Step 2: Use the mean formula. Mean = (2 + 4 + 6 + ... + 2n) / n Step 3: Factor out 2. Mean = 2(1 + 2 + ... + n) / n Step 4: Use 1 + 2 + ... + n = n(n + 1)/2…
Use the deviation method to find the mean of 4600, 5560, 6440, 4530, 7670, 6850, 6750, 7910, 5490, 6800.
Answer
Step 1: Choose an assumed mean. Take a = 6000. Step 2: Find deviations d_i = x_i - a. The deviations are -1400, -440, 440, -1470, 1670, 850, 750, 1910, -510, 800 Step 3: Add deviations. Σd_i = 2600 St…
A grouped distribution has class intervals 95-105, 105-115, 115-125, 125-135, 135-145, 145-155 with frequencies 9, 13, 26, 30, 12, 10. Find the mean by the direct method.
Answer
Step 1: Find class mid-points. 100, 110, 120, 130, 140, 150 Step 2: Multiply each midpoint by frequency. 9×100 = 900 13×110 = 1430 26×120 = 3120 30×130 = 3900 12×140 = 1680 10×150 = 1500 Step 3: Add p…
Why is the step-deviation method useful for grouped data with large values?
Answer
The step-deviation method makes calculations shorter by turning the deviations into small numbers. Method: 1. Choose assumed mean a. 2. Choose class-width h. 3. Compute u_i = (x_i - a) / h. 4. Use Mea…
For the data 3, 9, 5, 3, 11, 10, 17, 4, 7, 18, 21, find the median.
Answer
Step 1: Arrange in ascending order. 3, 3, 4, 5, 7, 9, 10, 11, 17, 18, 21 Step 2: Count values. n = 11, which is odd Step 3: Use median position. Median = ((n + 1) / 2)th term = 6th term Step 4: Identi…
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