Statistics — Practice

Question 1

Find mean: 2, 4, 6, 8, 10.

Accepted Answer

✦ Answer: Mean = (2+4+6+8+10)/5 = 30/5 = 6.

Question 2

Find mean of grouped data: Classes 0-10, 10-20, 20-30, 30-40 with frequencies 5, 8, 12, 5.

Accepted Answer

Step 1 — Class marks.
  x = 5, 15, 25, 35

Step 2 — fx.
  5×5=25, 8×15=120, 12×25=300, 5×35=175
  Σfx = 25+120+300+175 = 620

Step 3 — Σf.
  5+8+12+5 = 30

Step 4 — Mean.
  Mean = 620/30 ≈ 20.67

✦ Answer: Mean ≈ 20.67.

Question 3

Find median for grouped data: Classes 10-20, 20-30, 30-40, 40-50, 50-60 with frequencies 7, 10, 16, 12, 5.

Accepted Answer

Step 1 — Cumulative frequencies.
  CF: 7, 17, 33, 45, 50

Step 2 — N and N/2.
  N = 50; N/2 = 25

Step 3 — Median class.
  First CF ≥ 25 is 33 (in class 30-40).
  Median class: 30-40

Step 4 — Apply formula.
  l = 30, cf = 17 (before median class), f = 16, h = 10
  Median = 30 + ((25 − 17)/16) × 10
         = 30 + (8/16) × 10
         = 30 + 5
         = 35

Step 5 — Verify.
  Median should be in class 30-40 (yes, 35 is) ✓

✦ Answer: Median = 35.

Practice — Statistics

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