Stem and Leaf (Part 2) Worksheet with Answers

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2.16B Stem and Leaf (Part 2)

EDEXCEL 1MA1 · Calculator allowed · about 65 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

Kwame recorded, in minutes, how long 11 customers waited in a queue at a bakery one Saturday morning. The stem and leaf diagram shows his results.

0	3 3 6 8
1	0 2 4 4 7
2	1 5

Key: 1 | 0 means 10 minutes

(a)Write down the longest waiting time.(1)

(b)Write down how many customers waited less than 10 minutes.(1)

(c)Write down the number of customers who waited exactly 14 minutes.(1)

(Total for Question 1 is 3 marks)

2

Priya's parkrun time is recorded in a stem and leaf diagram as the row '4 | 2 2 5 9', where the stem shows the tens digit of her time in minutes and the leaf shows the units digit.Which of these is a correct key for this row?

A) 4 | 2 means 24 minutes
B) 4 | 2 means 42 minutes
C) 4 | 2 means 4.2 minutes
D) 4 | 2 means 4 minutes 2 seconds

(Total for Question 2 is 1 mark)

3

A stem and leaf diagram is being built to show the number of trees planted by different volunteer groups, where the stem shows the tens digit and the leaf shows the units digit.

(a)Write down the stem and the leaf for the value 36.(1)

(b)Write down the stem and the leaf for the value 8.(1)

(Total for Question 3 is 2 marks)

4

Erin has drawn a stem and leaf diagram to show the number of emails she received each day over 9 days.

0	4 7 9
1	2 3 3 5 8 21

Key: 1 | 2 means 12 emails

(a)Write down what is wrong with Erin's diagram.(1)

(b)Draw the diagram again with this corrected. Include the key.(2)

(Total for Question 4 is 3 marks)

5

The number of lengths swum by 10 members of a swimming club during one training session were:
14, 8, 21, 14, 9, 17, 23, 8, 19, 21

(a)Draw an ordered stem and leaf diagram to show this information. Use the stems 0, 1 and 2.(2)

(b)Write down a suitable key for your diagram.(1)

(Total for Question 5 is 3 marks)

6

The stem and leaf diagram shows the number of text messages sent in one day by each of 12 students in a class.

0	5 8
1	1 3 3 6 8 9
2	0 2 5 7

Key: 1 | 3 means 13 text messages

(a)Write down the modal number of text messages.(1)

(b)Find the median number of text messages.(2)

(c)Write down the range of the number of text messages.(1)

(Total for Question 6 is 4 marks)

7

The stem and leaf diagram shows the number of points scored by a school basketball team in each of 9 matches.

4	7
5	2 8 8
6	1 3 6
7	1 4

Key: 5 | 2 means 52 points
Work out the mean number of points scored. Give your answer correct to 1 decimal place.

(Total for Question 7 is 3 marks)

8

The times, in seconds, taken by 11 sprinters to run 100m in a school athletics trial were recorded:
11.8, 12.3, 13.1, 11.5, 12.9, 13.4, 11.5, 12.0, 13.8, 12.6, 11.2

(a)Draw an ordered stem and leaf diagram to show this information. Use the whole number of seconds as the stem and the first decimal digit as the leaf. Include a key.(3)

(b)Find the median time.(2)

(Total for Question 8 is 5 marks)

9

The number of minutes spent on homework one evening by 8 pupils in Class 9A and 8 pupils in Class 9B were recorded.
Class 9A: 25, 38, 19, 42, 31, 27, 33, 45
Class 9B: 21, 34, 46, 18, 29, 37, 41, 24

(a)Draw a back-to-back stem and leaf diagram to show this information. Use the stems 1, 2, 3 and 4. Include a key.(3)

(b)Find the range of homework times for Class 9B.(2)

(Total for Question 9 is 5 marks)

10

Use your diagram from Question 9 to answer this question.
Compare the average and the spread of the homework times for Class 9A and Class 9B.

(Total for Question 10 is 2 marks)

11

The stem and leaf diagram shows the number of visitors to a small museum on each of 9 days.

0	9
1	0 1 2 3 4 5 6
4	7

Key: 1 | 0 means 10 visitors

(a)Write down the value that is an outlier.(1)

(b)Find the range of the visitor numbers, not including the outlier.(2)

(c)Explain why the mean number of visitors is more affected by the outlier than the median.(1)

(Total for Question 11 is 4 marks)

12

The stem and leaf diagram shows the number of hours of overtime worked last month by each of 20 employees at a warehouse.

0	2 4 5 7 9
1	0 2 3 5 6 8 9
2	1 3 6 8
3	0 2 4 7

Key: 1 | 0 means 10 hours
Work out the percentage of employees who worked more than 25 hours of overtime last month.

(Total for Question 12 is 3 marks)

13

Fatima recorded, in minutes, how long she spent on 7 different apps on her phone yesterday. The stem and leaf diagram shows her results, but one leaf has been replaced with y.

0	2 5
1	3 6 6 9
2	y

Key: 1 | 3 means 13 minutes
The range of the times is 26 minutes.

(a)Find the value of y.(3)

(b)Hence write down the median number of minutes.(2)

(Total for Question 13 is 5 marks)

14

Noah calculated the mean number of minutes 6 students spent queuing for lunch, using the stem and leaf diagram below.

0	4 7
1	2 5 5
2	8

Key: 1 | 2 means 12 minutes
Noah's working: Sum = 4 + 7 + 12 + 15 + 15 + 28 = 81. Mean = 81 / 5 = 16.2

(a)Write down Noah's mistake.(1)

(b)Work out the correct mean.(2)

(Total for Question 14 is 3 marks)

15

The stem and leaf diagram shows the distances, in km, travelled on 9 long-distance train journeys taken by a school orchestra on tour. Because all the distances are over 100 km, the stem shows the first two digits (hundreds and tens) of each distance.

10	8
11	2 5 5
12	1 4 9
13	3 8

Key: 11 | 2 means 112 km

(a)Find the range of the distances.(2)

(b)Find the median distance.(2)

(Total for Question 15 is 4 marks)

16

Amelia recorded, in minutes, how long it took each of 7 friends to complete a jigsaw puzzle: 4, 5, 6, 6, 7, 8, 20.
First draw an ordered stem and leaf diagram for this data. Then show that the mean of these times is greater than the median.

(Total for Question 16 is 4 marks)

17

The stem and leaf diagram shows the number of pull-ups completed by 8 members of a gym class in a fitness test.

0	3 5 5 8
1	2 4
2	0 6

Key: 1 | 2 means 12 pull-ups
Which of these statements about the data is correct?

A) The mode is 8.
B) The median is 10.
C) The range is 20.
D) Exactly 3 members completed more than 15 pull-ups.

(Total for Question 17 is 1 mark)

18

The mean number of minutes spent waiting for a coffee by 6 customers at a cafe is 9.5 minutes. The stem and leaf diagram shows the waiting times, but one leaf is missing and shown as z.

0	3 6 8
1	2 z 5

Key: 1 | 2 means 12 minutes

(a)Find the value of z.(3)

(b)Write down the range of the waiting times.(1)

(Total for Question 18 is 4 marks)

Mark scheme · 2.16B Stem and Leaf (Part 2)

Question 1

(a) B1 25 cao
(a) Answer: 25 minutes
(b) B1 4 cao
(b) Answer: 4
(c) B1 2 cao
(c) Answer: 2

Question 2

B1 B cao
Answer: B

Question 3

(a) B1 stem 3, leaf 6 cao
(a) Answer: stem 3, leaf 6
(b) B1 stem 0, leaf 8 cao
(b) Answer: stem 0, leaf 8

Question 4

(a) B1 the value 21 has been written as a leaf in the stem 1 row; a leaf must be a single digit, so 21 needs its own stem 2 row with leaf 1 oe
(a) Answer: The value 21 has been added as a leaf (leaves must be single digits) instead of starting a new stem 2 row
(b) M1 attempt to move the value 21 into a new stem 2 row
(b) A1 fully correct diagram: 0 | 4 7 9, 1 | 2 3 3 5 8, 2 | 1 with a correct key
(b) Answer:
0 4 7 9
1 2 3 3 5 8
2 1
Key: 1 | 2 means 12 emails

0	4 7 9
1	2 3 3 5 8
2	1

Question 5

(a) M1 all 10 values correctly split into stem and leaf, any order within rows
(a) A1 leaves in each row fully ordered ascending: 0 | 8 8 9, 1 | 4 4 7 9, 2 | 1 1 3
(a) Answer:
0 8 8 9
1 4 4 7 9
2 1 1 3
(b) B1 correct key oe, e.g. 1 | 4 means 14 lengths
(b) Answer: 1 | 4 means 14 lengths

0	8 8 9
1	4 4 7 9
2	1 1 3

Question 6

(a) B1 13 cao
(a) Answer: 13
(b) M1 identifies the 6th and 7th values in the ordered list of 12 (16 and 18)
(b) A1 17 cao
(b) Answer: 17
(c) B1 22 cao
(c) Answer: 22

Question 7

M1 correctly sums all 9 values, e.g. 47+52+58+58+61+63+66+71+74 = 550
M1 divides their sum by 9
A1 61.1 awrt
Answer: 61.1 points (awrt)

Question 8

(a) M1 all 11 values correctly split into stem (whole seconds) and leaf (first decimal digit), any order
(a) A1 leaves in each row fully ordered ascending
(a) B1 correct key oe, e.g. 12 | 0 means 12.0 seconds
(a) Answer:
11 2 5 5 8
12 0 3 6 9
13 1 4 8
Key: 12 | 0 means 12.0 seconds
(b) M1 identifies the 6th value in the ordered list of 11
(b) A1 12.3 cao
(b) Answer: 12.3 seconds

11	2 5 5 8
12	0 3 6 9
13	1 4 8

Question 9

(a) M1 all 8 Class 9A values correctly placed as leaves, any order
(a) M1 all 8 Class 9B values correctly placed as leaves, any order
(a) A1 both sides fully ordered correctly with a correct key
(a) Answer:
Class 9A Stem Class 9B
9 1 8
7 5 2 1 4 9
8 3 1 3 4 7
5 2 4 1 6
Key: for Class 9A, 9 | 1 means 19 minutes. For Class 9B, 1 | 8 means 18 minutes.
(b) M1 46 - 18
(b) A1 28 cao
(b) Answer: 28 minutes

Class 9A	Stem	Class 9B
9	1	8
7 5	2	1 4 9
8 3 1	3	4 7
5 2	4	1 6

Question 10

B1 ft correct comparison of an average in context, e.g. the mean homework time for Class 9A (32.5 minutes) is higher than for Class 9B (31.25 minutes), so Class 9A tends to spend slightly longer on homework oe
B1 ft correct comparison of the spread in context, e.g. the range for Class 9B (28 minutes) is slightly greater than for Class 9A (26 minutes), so Class 9B's homework times are slightly more spread out oe
Answer: Class 9A has a higher mean homework time (32.5 minutes vs 31.25 minutes for Class 9B), but Class 9B has a slightly larger range (28 minutes vs 26 minutes for Class 9A), so Class 9B's homework times are slightly more spread out.

Question 11

(a) B1 47 cao
(a) Answer: 47 visitors
(b) M1 16 - 9
(b) A1 7 cao
(b) Answer: 7 visitors
(c) B1 correct reason referring to how each average uses the data, e.g. the mean uses every value in its calculation so the large outlier pulls it up, whereas the median only depends on the middle value(s) and is barely affected by how large the outlier is oe
(c) Answer: The mean uses every value, so the outlier of 47 pulls it up a lot; the median only depends on the middle value(s), so it barely changes because of the outlier

Question 12

M1 identifies the values greater than 25 as 26, 28, 30, 32, 34 and 37
M1 forms 6/20 (or equivalent) for the proportion of employees
A1 30% cao
Answer: 30%

Question 13

(a) M1 recognises that the minimum value is 2, so the maximum must be 2 + 26 = 28
(a) M1 sets up 20 + y = 28 (or equivalent reasoning)
(a) A1 y = 8 cao
(a) Answer: y = 8
(b) M1 identifies the 4th value in the ordered list of 7
(b) A1 16 cao
(b) Answer: 16 minutes

Question 14

(a) B1 he divided the total by 5 instead of 6, since there are 6 values in the data set oe
(a) Answer: He divided the total by 5 instead of 6 (there are 6 values in the data)
(b) M1 81 / 6
(b) A1 13.5 cao
(b) Answer: 13.5 minutes

Question 15

(a) M1 138 - 108
(a) A1 30 cao
(a) Answer: 30 km
(b) M1 identifies the 5th value in the ordered list of 9
(b) A1 121 cao
(b) Answer: 121 km

Question 16

M1 attempts an ordered stem and leaf diagram (0 | 4 5 6 6 7 8, 2 | 0) or ordered list, and identifies the median as 6
M1 correctly sums the data: 4+5+6+6+7+8+20 = 56
A1 mean = 56/7 = 8
C1 correct conclusion comparing both values, e.g. 8 > 6, so the mean is greater than the median cso
Answer: Mean = 8 minutes, median = 6 minutes, and 8 > 6, so the mean is greater than the median.

Question 17

B1 B cao
Answer: B

Question 18

(a) M1 total sum = mean x number of values = 9.5 x 6 = 57
(a) M1 forms 44 + (10+z) = 57 (or equivalent), using the 5 known values summing to 44
(a) A1 z = 3 cao
(a) Answer: z = 3
(b) B1 12 cao
(b) Answer: 12 minutes

Stem and Leaf (Part 2) - Worksheets, Questions and Revision

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2.16B Stem and Leaf (Part 2)

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