Statistics — Practice

Question 1

Find the mean of 25, 30, 35, 40, 45.

Accepted Answer

Step 1 — Sum all observations.
  25 + 30 + 35 + 40 + 45 = 175.

Step 2 — Divide by n = 5.
  Mean = 175 / 5 = 35.

✦ Answer: Mean = 35.

Question 2

Find the median of 11, 7, 14, 8, 21, 5, 17.

Accepted Answer

Step 1 — Sort in ascending order.
  5, 7, 8, 11, 14, 17, 21.

Step 2 — n = 7 (odd). Middle position = (7+1)/2 = 4th observation.

Step 3 — 4th observation = 11.

✦ Answer: Median = 11.

Question 3

Find the mode of 2, 3, 3, 4, 5, 3, 6, 7.

Accepted Answer

Step 1 — Count frequencies: 2→1, 3→3, 4→1, 5→1, 6→1, 7→1.

Step 2 — 3 occurs 3 times; all others occur once.

✦ Answer: Mode = 3.

Question 4

The mean of 5 numbers is 18. If one number is added and the new mean becomes 20, find the added number.

Accepted Answer

Step 1 — Find original sum.
  Original sum = 5 × 18 = 90.

Step 2 — Find new sum.
  New sum = 6 × 20 = 120.

Step 3 — Added number = 120 − 90 = 30.

✦ Answer: The added number is 30.

Question 5

20 students scored: 7, 8, 9, 7, 6, 8, 9, 5, 7, 8, 9, 7, 6, 5, 8, 9, 7, 7, 6, 8. Build a frequency table and find the mode.

Accepted Answer

Step 1 — Build the frequency table.
  Score 5: appears 2 times
  Score 6: appears 3 times
  Score 7: appears 6 times
  Score 8: appears 5 times
  Score 9: appears 4 times
  Total: 20 ✓

Step 2 — Identify highest frequency: 6 (for score = 7).

✦ Answer: Mode = 7.

Question 6

Explain the difference between a bar graph and a histogram. When would you use each?

Accepted Answer

Step 1 — Bar graph: bars WITH GAPS; used for discrete or CATEGORICAL data (e.g., favourite colours of students). The gap indicates that values in between are not possible.

Step 2 — Histogram: bars WITHOUT GAPS; used for CONTINUOUS (grouped/interval) data (e.g., heights in cm class-wise). The no-gap shows continuity of the data.

✦ Answer: Use bar graph for discrete/categorical data. Use histogram for continuous grouped data.

Question 7

The mean of 30 observations is 20 and the mean of 20 other observations is 25. Find the combined mean of all 50 observations.

Accepted Answer

Step 1 — Find the sum of the first group.
  Sum₁ = 30 × 20 = 600.

Step 2 — Find the sum of the second group.
  Sum₂ = 20 × 25 = 500.

Step 3 — Combined sum = 600 + 500 = 1100. Combined n = 30 + 20 = 50.

Step 4 — Combined mean = 1100 / 50 = 22.

✦ Answer: Combined mean = 22.

Practice — Statistics

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