KS3 Maths · Year 8 · Chapter 4: Using data · Lesson 5

Statistical investigations

Year 8About 60 minutesNo calculator45 marks

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Quick questions to start.

A1
Last lesson
The cumulative frequencies of $40$ times are $6$ , $15$ , $28$ , $36$ and $40$ . How many times are in the third class?
[1 mark]
Answer
A2
Needed today
Work out the median of $7$ , $3$ , $9$ , $4$ and $12$ .
[1 mark]
Answer
A3
Needed today
Work out the mean of $12$ , $15$ , $9$ and $14$ .
[1 mark]
Answer
A4
From chapter 2
Expand $4 (3 x - 2)$ .
[1 mark]
Answer

Example, then your turn

Year 8

Your teacher works through each example with you. Then try the one beside it.

Example 1

Maya asks, "Do people with longer legs jump further?" (i) Write a hypothesis she could test. (ii) Should she use primary or secondary data? Why?

Hint A hypothesis is a statement, not a question. It says what you think will happen.

B1
Jack asks, "Does more sleep help students do well in a times-table test?" (i) Write a hypothesis he could test. (ii) Write down the two things he must record for each student.
[2 marks]

Example 2

The table shows the students in each year group of a school. Lucy wants a sample of $60$ students, with the same proportion from each year group. How many should she choose from each year group?

Hint Work out what fraction of the school she will choose. Then take that fraction of each year group.

B2
A chess club has $135$ junior and $225$ senior members. Omar wants a sample of $40$ members, with the same proportion of juniors and seniors as the club. How many juniors and how many seniors should he choose?
[2 marks]
Answerjuniors $\dots\dots$ seniors $\dots\dots$

Example 3

Hypothesis: "The warmer a table-tennis ball is, the higher it bounces." Ben drops a ball $5$ times at each temperature. The table shows the bounce heights in centimetres. Work out the mean height at each temperature. Does the data support the hypothesis?

Hint Add the five heights in each column and divide by

5

B3
Hypothesis: "The more fertiliser a plant is given, the taller it grows." The table shows the heights, in centimetres, of $5$ plants in each group. Work out the mean height for each group. Does the data support the hypothesis? Give a reason.
[4 marks]

Example 4

Hypothesis: "Older students estimate $30$ seconds better." Each student says "stop" when they think $30$ s have passed. Year 7 (s): $34$ , $22$ , $40$ , $27$ , $45$ , $25$ , $38$ . Year 11 (s): $31$ , $26$ , $33$ , $29$ , $35$ , $28$ , $30$ . Compare the medians and ranges. Does the data support the hypothesis?

Hint Put each list in order. The median is the middle (4th) time.

B4
Hypothesis: "Students react faster after practice." In a ruler-drop test, a shorter distance is a faster reaction. Before (cm): $18$ , $24$ , $15$ , $21$ , $27$ , $12$ , $19$ . After (cm): $14$ , $16$ , $11$ , $17$ , $13$ , $15$ , $19$ . Work out each median. Does the data support the hypothesis? Give a reason.
[3 marks]

Practice

Year 8

C1
Sam times students solving a puzzle. Most take $1$ to $3$ minutes. He records each time to the nearest minute. Explain why this is not good, and suggest a better accuracy.
[2 marks]
C2
Kai makes this collection sheet for times from $20$ to $40$ seconds. Give one problem with the classes, and say how to fix it.
[2 marks]

C3
Zara's hypothesis is "Most students at my school walk to school." She asks the $30$ students in her tutor group, who all live near the school. Give two reasons why her sample is not good.
[2 marks]
C4
Lily's walking times, in minutes, are $12$ , $14$ , $13$ , $15$ , $14$ , $52$ . Which average should she use? Give a reason, and work it out.
[2 marks]

Exam-style questions

GCSE Foundation

D1
Leo tests the hypothesis "Girls read for longer than boys." He asks $8$ girls and $5$ boys how many minutes they read yesterday. Girls: $25$ , $40$ , $20$ , $35$ , $30$ , $15$ , $45$ , $30$ . Boys: $35$ , $40$ , $25$ , $45$ , $30$ . Leo says, "The girls read for $240$ minutes in total and the boys for $175$ , so girls read more."
Show that Leo is wrong. You must show your working.
[4 marks]

D2
Lena wants to find out how much time students spend on homework. She writes this question with three response boxes: "How much time do you spend on homework?"
(a)
Write down two things wrong with her question or her response boxes.
[2 marks]
(b)
Write a better question for Lena, with response boxes.
[2 marks]
Total for D2: 4 marks
D3
Hypothesis: "Year 9 students can hold their breath for longer than Year 7 students." The table shows the times, in seconds, for $9$ students from each year.
(a)
Work out the median time for each year group.
[2 marks]
AnswerYear 7 $\dots\dots$ s Year 9 $\dots\dots$ s
(b)
Work out the range for each year group.
[1 mark]
AnswerYear 7 $\dots\dots$ s Year 9 $\dots\dots$ s
(c)
Does the data support the hypothesis? Give a reason, and make one comparison of the spread.
[2 marks]
Total for D3: 5 marks
D4
A sports centre has $1200$ members. The table shows its three groups of members. The manager wants a sample of $80$ members, with the same proportion from each group.
(a)
Work out how many members from each group should be in the sample.
[3 marks]
AnswerAdults $\dots\dots$ Juniors $\dots\dots$ Seniors $\dots\dots$
(b)
Karim says, "I will ask the first $80$ people who come in on Monday morning." Give one reason why his sample may not represent all the members.
[1 mark]
Total for D4: 4 marks

Extension

Stretch

No route is given. The hints are at the end of the sheet. Use one at a time.

E1
Ali drops a ball $5$ times at $40$ °C and $5$ times at $60$ °C. Heights are whole numbers of centimetres. One height at $60$ °C, $x$ cm, was lost. The table shows the heights in centimetres. Ali says the data supports "warmer balls bounce higher" only if BOTH the mean and the median at $60$ °C are higher than at $40$ °C. Work out the smallest value of $x$ that does this.
[5 marks]
Hint 1 · What to try
Find the mean and median at $40$ °C.
Hint 2 · The first line
Mean $48$ , median $47$ . Mean: $198 + x > 240$ .
Hint 3 · The full method
Mean: $x \geq 43$ . Median: $x > 47$ . Both: $x \geq 48$ .
Answer

How did it go?

Colour one circle on each line.

	Not yet	Nearly	Yes
I can write a hypothesis and plan the data.
I can choose a fair, proportional sample.
I can test a hypothesis with averages and range.

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