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Statistical diagrams 2.pptx
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Statistical diagrams 2
Interpreting and representing data
Lesson 6 of 6
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson
Interpreting and representing data
Lesson 6 of 6
Answer each one, then check.
1
Find the median of 3, 5, 8, 10.
2
What is the range of 12, 4, 19, 7?
3
What is a modal class?
4
What is the midpoint of the class 20 < t ≤ 30?
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Last Lesson - Answers
Interpreting and representing data
Lesson 6 of 6
1
Find the median of 3, 5, 8, 10.
6.5 - the mean of 5 and 8.
2
What is the range of 12, 4, 19, 7?
19 − 4 = 15
3
What is a modal class?
The class with the highest frequency.
4
What is the midpoint of the class 20 < t ≤ 30?
25
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Learning Objectives
Interpreting and representing data
Lesson 6 of 6
1
Draw and read an ordered stem-and-leaf diagram, with a key.
2
Find averages and the range from a stem-and-leaf diagram.
3
Draw a frequency polygon for grouped data.
4
Compare two sets of data using an average and the range.
5
Recognise graphs that are misleading.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Stem-and-Leaf Diagrams
Interpreting and representing data
Lesson 6 of 6
A stem-and-leaf diagram sorts data into order while keeping every value.
Stem and leaf
Split each value: for 73, the stem is 7 (the tens) and the leaf is 3 (the units).
Ordered
Write the leaves in order from smallest to largest along each row.
Key
Always include one, such as "7 then 3 means 73 beats per minute", written with a bar between the stem and the leaf.
Shape
Turned on its side, it looks like a bar chart of the data.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Resting Pulse Rates of 15 People
Interpreting and representing data
Lesson 6 of 6
Key: 7 then 3 means 73 beats per minute.
Stem
Leaves
5
8
6
2 5 7
7
0 1 1 3 6 8
8
0 2 5
9
1 4
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Reading a Stem-and-Leaf Diagram
Interpreting and representing data
Lesson 6 of 6
Use the pulse rate diagram to find the median, the mode and the range.
1
Count the values
1 + 3 + 6 + 3 + 2 = 15, so the median is the 8th value
2
Count along the leaves to the 8th
58, 62, 65, 67, 70, 71, 71, 73
3
The mode: the only repeated value
71
4
The range: largest − smallest
94 − 58 = 36
ANSWER
Median 73, mode 71, range 36 beats per minute
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Back-to-Back Stem-and-Leaf Diagrams
Interpreting and representing data
Lesson 6 of 6
Two sets of data share one stem, with one set's leaves on each side.
Layout
The stem runs down the middle. The leaves of one set go to the right; the other set's go to the left.
Reading the left side
The leaves on the left are read from the stem outwards: a leaf 4 by stem 6 on the left means 64.
Two keys
One for each side, so there is no confusion.
Why
Two groups can be compared at a glance - for example, pulse rates before and after exercise.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART TWO
Frequency Polygons
Grouped data drawn as a line.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Drawing a Frequency Polygon
Interpreting and representing data
Lesson 6 of 6
A frequency polygon plots the midpoint of each class against its frequency.
Midpoints
Work out the midpoint of each class.
Plot
Plot (midpoint, frequency) for each class.
Join
Join the points with straight lines. Do not join the last point back to the first.
Compare
Two frequency polygons on the same axes compare two sets of data clearly.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
A Frequency Polygon
Interpreting and representing data
Lesson 6 of 6
Each point sits above the middle of its class.
This is the journey time data from last lesson. The peak at 15 minutes shows the modal class, 10 < t ≤ 20, straight away. Drawing a second polygon on the same axes - say, for another year group - would let you compare the two.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Comparing Distributions
Interpreting and representing data
Lesson 6 of 6
To compare two sets of data, always compare an average AND a measure of spread - in context.
An average
"The median pulse rate after exercise (112) is higher than before (73), so pulse rates were higher on average after exercise."
The spread
"The range after exercise (22) is smaller than before (36), so the pulse rates after exercise were more consistent."
In context
Use the words of the question: "pulse rates", not "the data".
Two sentences
One for the average, one for the spread - that is what most mark schemes want.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
PART THREE
Misleading Graphs
How a graph can give the wrong impression.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Spot the Trick
Interpreting and representing data
Lesson 6 of 6
The same numbers, two very different impressions.
Sales rose from 92 to 98 - about 6%. Start the axis at 90 and the rise looks enormous. Look out for axes that do not start at zero, uneven scales, missing labels, and 3D charts that make the nearest sections look bigger.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Key Terms
Interpreting and representing data
Lesson 6 of 6
Stem-and-leaf diagram
A diagram that orders data by splitting each value into a stem and a leaf.
Key
The line that explains how to read a diagram, e.g. 7 then 3 means 73.
Frequency polygon
A graph joining points plotted at the midpoints of classes against their frequencies.
Distribution
How the values of a set of data are spread out.
Misleading graph
A graph that gives a false impression of the data.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Interpreting and representing data
Lesson 6 of 6
YOUR TASK
Before and After
15 minutes
Measure your resting pulse for 15 seconds and multiply by 4. Then do 1 minute of star jumps and measure it again. Collect the class results and draw a back-to-back stem-and-leaf diagram of "before" and "after". Find the median and range of each, and write two sentences comparing them.
1
Collect the data.
2
Draw the back-to-back diagram with keys.
3
Find the median and range of each.
4
Compare in two sentences.
WHAT A GOOD ANSWER SHOWS
A back-to-back diagram with ordered leaves and two keys; medians and ranges for both sets; one comparison of the medians and one of the ranges, both in context.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Can I...?
Interpreting and representing data
Lesson 6 of 6
Draw an ordered stem-and-leaf diagram with a key.
Find the median and range from a stem-and-leaf diagram.
Read a back-to-back stem-and-leaf diagram.
Draw a frequency polygon.
Compare two data sets using an average.
Compare two data sets using the range.
Write comparisons in context.
Explain why a graph is misleading.
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EDEXCEL GCSE MATHS · FOUNDATION & HIGHER
Summary & Exam Focus
Stem-and-leaf: ordered leaves and a key; it keeps every value.
Frequency polygon: plot (midpoint, frequency) and join with straight lines.
Compare with an average AND a measure of spread, in context.
Misleading graphs: check that the axes start at zero and the scales are even.
EXAM FOCUS
Compare the times taken by the two groups. (2 marks)
Two marks means two comparisons: one about an average (which is higher) and one about the spread (which is more consistent), both in the context of the question.
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