Grouped Data, Percentiles & Modal Interval (Grade 10) — Worksheet & Memo

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Grade 10 · Statistics

Grouped Data, Percentiles & Modal Interval (Grade 10)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 21

Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.

1
Write down the midpoint of the interval 20 ≤ x < 30.
(1)
(20 + 30)/2 = 25✓ (1)
2
Using the table (f = 4, 9, 14, 8, 5 for intervals of width 10 from 0), estimate the mean.
(4)
(1 010)/40 = 25,25✓✓✓✓ (4)
3
Write down the modal interval for that data.
(1)
20 ≤ x < 30 (highest frequency, 14)✓ (1)
4
In which interval does the median lie for that data?
(2)
The 20th value → 20 ≤ x < 30✓✓ (2)
5
Determine the position of the 25th percentile when n = 40.
(2)
25/100 × 40 = the 10th value✓✓ (2)
6
Q₁ = 24 and Q₃ = 42. Calculate the interquartile range.
(1)
42 − 24 = 18✓ (1)
7
Q₁ = 24 and Q₃ = 42. Calculate the semi-interquartile range.
(2)
18/2 = 9✓✓ (2)
8
Why can the mean of grouped data only be estimated?
(2)
Because the individual values are unknown — we assume each one sits at its interval's midpoint.✓✓ (2)
9
State TWO differences between a histogram and a bar graph.
(2)
A histogram shows continuous grouped data and a bar graph shows categorical data ✓; the bars of a histogram touch while those of a bar graph have gaps ✓(2)
10
The bars of a histogram have frequencies 6, 10, 14, 9 and 5. How many values are in the data set, and which is the modal interval?
(2)
6 + 10 + 14 + 9 + 5 = 44 values ✓; the modal interval is the one with frequency 14 ✓(2)
11
Explain why the bars of a histogram must touch.
(2)
The intervals are continuous ✓ — one interval ends exactly where the next begins, so there is no value that could fall in a gap ✓(2)

TOTAL: 21 marks