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

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Grade 10 · Statistics

Grouped Data, Percentiles & Modal Interval (Grade 10)

EXAM-STYLE CLASS TEST

Marks

Duration

40 minutes

Questions

Name:

Class:

Date:

Mark

/ 26

Instructions and Information

Answer ALL the questions in this question paper.
Answer QUESTION 1 by circling the letter (A–D) in the answer grid at the end of that section.
Show ALL calculations clearly.
Show all units where applicable.
Number the answers correctly according to the numbering system used in this question paper.
A non-programmable calculator may be used, unless stated otherwise.
Write neatly and legibly.

Question 1

[10 MARKS]

Four options are given as possible answers to the following questions. Choose the correct answer and circle the letter (A–D) in the grid at the end of this section. If you want to change your choice, put a cross through the wrong letter and circle your new choice.

1.1
For the interval 20 ≤ x < 30, the MIDPOINT used to estimate the mean is …
(1)
A)25
B)30
C)20
D)10
1.2
The MODAL interval is the one with …
(1)
A)the highest frequency
B)the largest midpoint
C)the widest class
D)the middle position
1.3
Marks are grouped as 0 − 20 (f = 4), 20 − 40 (f = 9), 40 − 60 (f = 12) and 60 − 80 (f = 5). The MODAL interval is …
(1)
A)40 − 60
B)20 − 40
C)60 − 80
D)0 − 20
1.4
For that grouped data, the total number of learners is …
(1)
A)30
B)26
C)20
D)12
1.5
For that grouped data, the interval containing the MEDIAN is …
(1)
A)40 − 60
B)20 − 40
C)0 − 20
D)60 − 80
1.6
For that grouped data, the ESTIMATED MEAN is …
(1)
A)42
B)40
C)50
D)1 260
1.7
The mean of grouped data is only an ESTIMATE because …
(1)
A)the original values inside each interval are unknown
B)the frequencies are guesses
C)the intervals are unequal
D)a mean is always approximate
1.8
The 25th percentile of a data set is the same as …
(1)
A)Q₁
B)the median
C)Q₃
D)the mode
1.9
The SEMI-interquartile range is …
(1)
A)Q₃ − Q₁2
B)Q₃ − Q₁
C)Q₃ + Q₁2
D)Q₃ × Q₁
1.10
If Q₁ = 18 and Q₃ = 34, the semi-interquartile range is …
(1)
A)8
B)16
C)26
D)52

Answer grid — circle your answers for Question 1

1.1	A	B	C	D
1.2	A	B	C	D
1.3	A	B	C	D
1.4	A	B	C	D
1.5	A	B	C	D
1.6	A	B	C	D
1.7	A	B	C	D
1.8	A	B	C	D
1.9	A	B	C	D
1.10	A	B	C	D

Question 2

[16 MARKS]

The table below shows the times, in minutes, taken by 50 learners to complete a task.

Time (min)	0 ≤ t < 10	10 ≤ t < 20	20 ≤ t < 30	30 ≤ t < 40	40 ≤ t < 50
Frequency	4	8	15	14	9

2.1
Complete a cumulative frequency table for the data.
(3)
2.2
Calculate the estimated mean, using the midpoint of each interval.
(4)
2.3
Determine the position of the LOWER QUARTILE, and the interval in which it lies.
(3)
2.4
If Q₁ = 21 and Q₃ = 37, calculate the interquartile range and the semi-interquartile range, and state what the semi-interquartile range measures.
(3)
2.5
Explain ONE advantage and ONE disadvantage of grouping data in this way.
(3)

TOTAL: 26 marks

This question paper consists of 2 questions.