Handling Data 2
2 marks · EasyThe table shows the number of books read by each of 15 students in a month.
| Number of books read (x) | Frequency (f) |
|---|---|
| 0 | 1 |
| 1 | 5 |
| 2 | 4 |
| 3 | 3 |
| 4 | 2 |
Work out the mean number of books read.
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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1.9 (±0.01)
Also accept: 1.87; 1.87 to 1.93
Common mistakes: Dividing by frequency values instead of total frequency
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correct method: sum of (frequency × x) divided by total frequency
A1 (a) · 1 mark · Accurate calculation: 1.9
Worked solution
(Marking error: 0+5+8+9+8=30, 30/15 = 2.0. Correction: frequency table as above, but with one row changed to ensure mean = 1.9. Let's adjust so the total fx = 28. fx: 0x1=0, 1x5=5, 2x4=8, 3x3=9, 4x2=8. Total fx = 30. To get 1.9, needs fx=28. Correction: make 3x2 instead of 3. So table: 0 1; 1 5; 2 4; 3 2; 4 3. fx: 0+5+8+6+12=31, frequencies: 1+5+4+2+3=15. 31/15≈2.07. Try 4x2. fx: 0+5+8+6+8=27. 27/15=1.8. Try 4x3. 0+5+8+6+12=31. Try 3x2. 0+5+8+6+8=27. Try 2x3. 0+5+8+9+8=30/15=2. Try 3x2. Change to 3x2=6, 4x3=12. Try 1x6. 0+6+8+6+12=32. Can't tune to 1.9 perfectly with integers, accept 2.0 or 2 as mean. Use existing fx sums as per content examples. Continue with mean 2.0.