These eight questions use one data set. The weights of 30 parcels, in kg, are grouped as 1 to 10 (3 parcels), 11 to 20 (7), 21 to 30 (12), 31 to 40 (6) and 41 to 50 (2). Try each on paper first.
Questions
Question 1. State the boundaries and the size of the class 21 to 30 (2 marks).
Answer
Lower boundary 20.5 and upper boundary 30.5. The class size is 30.5 − 20.5 = 10.
Question 2. Write the cumulative frequency column (2 marks).
Answer
3, 10, 22, 28, 30. The last value equals the total of 30.
Question 3. State the modal class (1 mark).
Answer
The highest frequency is 12, so the modal class is 21 to 30.
Question 4. Estimate the mean weight (3 marks).
Answer
Midpoints: 5.5, 15.5, 25.5, 35.5, 45.5. Products: 16.5, 108.5, 306, 213, 91. Σfx = 735.
Mean = 735 ÷ 30 = 24.5 (estimate).
Question 5. List the points you would plot for the ogive (2 marks).
Answer
(0.5, 0), (10.5, 3), (20.5, 10), (30.5, 22), (40.5, 28), (50.5, 30). The first point is the zero start at the lower boundary of the first class.
Question 6. From the ogive, estimate the median and the interquartile range (4 marks).
Answer
The median is at 15, between (20.5, 10) and (30.5, 22): 20.5 + (5 ÷ 12) × 10 ≈ 24.7.
Q1 is at 7.5: 10.5 + (4.5 ÷ 7) × 10 ≈ 16.9. Q3 is at 22.5: 30.5 + (0.5 ÷ 6) × 10 ≈ 31.3.
The interquartile range is 31.3 − 16.9 = 14.4.
Question 7. Estimate how many parcels weigh more than 35 (2 marks).
Answer
At 35 the ogive reads 22 + (4.5 ÷ 10) × 6 = 24.7, so about 25 parcels weigh up to 35. Then 30 − 25 = 5 parcels weigh more than 35 (approximately).
Question 8. A second batch of 30 parcels has a median of 24.5 and an interquartile range of 8.0. Compare it with the first batch (3 marks).
Answer
The medians are similar (24.7 and 24.5), so the centres are close. The interquartile range of the second batch (8.0) is smaller than that of the first (14.4).
So the weights in the second batch are more consistent.
If you got these wrong
Questions 1 to 3 use reading class intervals and cumulative frequency. Question 4 uses estimating mean from grouped data.
Questions 5 to 7 use constructing and interpreting an ogive. Question 8 uses comparing grouped data using quartiles and spread.
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