Collect, Organise & Summarise Data (Grade 9) — Worksheet & Memo

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Grade 9 · Data Handling

Collect, Organise & Summarise Data (Grade 9)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 36

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
The mean of 45, 52, 61, 48, 54 and x is 52. Solve for x.
(3)
(45 + 52 + 61 + 48 + 54 + x)/6 = 52 (1)
260 + x = 52 × 6 = 312 (1)
x = 312 − 260 = 52 (1)✓✓✓ (3)
2
What is the difference between a population and a sample?
(2)
The population is the whole group; the sample is the smaller part actually surveyed.✓✓ (2)
3
Why is surveying only your friends about school food biased?
(2)
They are not representative of the whole school.✓✓ (2)
4
What is wrong with the intervals 0–10, 10–20, 20–30?
(2)
They overlap — 10 and 20 each fit two intervals.✓✓ (2)
5
How do a histogram and a bar graph differ?
(2)
Histogram bars touch (continuous data); bar-graph bars have gaps (separate categories).✓✓ (2)
6
In the histogram above, which is the modal class?
(1)
20–29, with a frequency of 9✓ (1)
7
In the histogram above, how many values are there in total?
(2)
3 + 7 + 9 + 5 + 2 = 26✓✓ (2)
8
Find the mean of R8 000, R9 000, R9 500, R10 000 and R80 000.
(3)
116 500 ÷ 5 = R23 300✓✓✓ (3)
9
Find the median of that same salary data.
(2)
R9 500✓✓ (2)
10
Which average is fairer for that salary data, and why?
(2)
The median — the R80 000 outlier pulls the mean far above what almost everyone earns.✓✓ (2)
11
Give TWO reasons why a double bar graph is better than two separate bar graphs for comparing boys and girls.
(2)
Both groups share one scale so the comparison is fair ✓; the pairs sit side by side so differences can be read directly ✓(2)
12
The double bar graph below shows the sports played by a group of learners. State the difference between the number of girls and the number of boys who play netball, and one thing the graph does NOT tell you.
(2)
Difference = 10 ✓; it does not show the total surveyed / whether learners play more than one sport ✓(2)
13
Explain how two separate bar graphs could be used to mislead a reader.
(2)
If the two graphs use different vertical scales ✓, a smaller quantity can be drawn taller than a larger one, so the comparison looks the opposite of the truth ✓(2)
14
In a spelling test the boys’ mean was 71% and the girls’ mean was 78%. Write a conclusion that would earn full marks.
(2)
The girls scored higher, with a mean of 78% against the boys’ 71% ✓ — a difference of 7 percentage points, for the learners in this test only ✓(2)
15
A shop’s sales were 48, 54, 60 and 66 items over four weeks. Predict week 5 and state the assumption you are making.
(3)
The difference is a constant 6 ✓; 66 + 6 = 72 items ✓; this assumes the trend of +6 a week continues ✓(3)
16
A learner surveys 20 friends and reports that “most learners at the school play soccer”. Give TWO reasons to question this conclusion.
(2)
The sample is only 20 learners, far too few for the whole school ✓; they are all the learner's friends, so they are not representative — friends tend to share interests ✓(2)
17
A bar graph’s vertical axis starts at 40 instead of 0. Explain how this could mislead a reader.
(2)
The bars only show the part above 40, so small differences are stretched to look large ✓; a reader glancing at the heights would think one group is far bigger than another when the real gap is small ✓(2)

TOTAL: 36 marks