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Histograms
Histograms are different to bar charts. Bar charts are frequency diagrams
that show categories along the horizontal axis, whereas histograms are
frequency diagrams that show grouped data values along the horizontal axis.
Histograms can be used to show both discrete and continuous data.
Bar
Number of pets
owned.
Frequency
Meals sold
during the week.
Frequency
Frequency
Pupils travelling
to school
Charts
Car
Bike
Bus
Walk
MT W T F S S
Categories
1 2 3 4 5 6 6+
Number category
directly underneath
middle of bar.
Histograms
Histograms are different to bar charts. Bar charts are frequency diagrams
that show categories along the horizontal axis, whereas histograms are
frequency diagrams that show grouped data values along the horizontal axis.
Histograms can be used to show both discrete and continuous data.
Bar
Number of pets
owned.
Frequency
Charts
MT W T F S S
Histograms
Grouped
Data
0-9 10-19 20-29 30-39 40-49 50-59
Runs
Discrete data.
1 2 3 4 5 6 6+
Maximum
daytime
Temperature
Frequency
Car
Bike
Bus
Walk
Runs scored in matches by a
batsman last season.
Frequency
Meals sold
during the week.
Frequency
Frequency
Pupils travelling
to school
10
14
18 22 26 28
Temperature (oC)
32
Continuous data
Histograms for Discrete Data
Use the histogram to determine how many cricket matches the
batsman played last season.
Frequency
20
Runs scored by an opening batsman in
40
one-day cricket matches last season.
16
15
9
10
8
5
5
2
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
Use the histogram to determine how many times the batsman
scored 40 runs or more.
20
Runs scored by an opening batsman in
26
one-day cricket matches last season.
Frequency
16
15
10
8
5
2
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
Use the histogram to determine how many times the batsman
scored less than 60 runs.
20
Runs scored by an opening batsman in
30
one-day cricket matches last season.
Frequency
16
15
9
10
5
5
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
The histogram shows that the batsman scored between 40 and 59
runs in most of his matches. True or false? Discuss
Frequency
20
15
Runs scored by an opening batsman in
one-day cricket matches last season.
False: He scored that
many runs in only 16
out of 40 matches.
10
5
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
The histogram shows that the batsman scored 50 runs in some of
the matches. True or false? Discuss
20
Runs scored by an opening batsman in
one-day cricket matches last season.
Frequency
False
15
10
5
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
The histogram shows that the batsman scored some runs in every
match. True or false? Discuss
20
Runs scored by an opening batsman in
one-day cricket matches last season.
Frequency
False
15
10
5
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data
The histogram shows that the batsman scored more than 39 runs in
most of his matches. True or false? Discuss
Frequency
20
15
Runs scored by an opening batsman in
one-day cricket matches last season.
True: He scored more
than 39 runs in 26 out
of 40 matches.
10
5
0 - 19 20 - 39 40 - 59 60 - 79 80 - 100
Runs Scored
Histograms for Discrete Data(2)
The histogram below shows the number of marks scored in a
maths test by some students.
25
Test Scores
Frequency
20
15
10
5
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Histograms for Discrete Data(2)
Use the histogram to determine how many students passed
the test if the pass mark was 30.
25
Test Scores
23
Frequency
20
14
15
8
10
5
1
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Histograms for Discrete Data(2)
Use the histogram to determine how many students got less
than 20 marks.
25
Test Scores
19
Frequency
20
15
15
10
5
4
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Histograms for Discrete Data(2)
The Histogram shows that some students scored 25 marks in
the test. True or false? Discuss.
25
Test Scores
False
Frequency
20
15
10
5
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Histograms for Discrete Data(2)
The Histogram shows that most students scored between 20
to 29 marks in the test. True or false? Discuss.
25
False: Only 23 out of
65 out of scored
Test Scores
within this range.
Frequency
20
15
10
5
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Histograms for Discrete Data(2)
Since the pass mark for this test was a score of 30, discuss
whether you think the test was easy or hard.
25
The test was hard
since only 23/65
students passed the
test. Most of them
failed!
Test Scores
Frequency
20
15
10
5
0-9
10 - 19
20 - 29
30 - 39
Marks
40 - 49
50 - 60
Drawing a Histogram from raw data.
The following data shows the number of runs scored by an
opening batsman during matches last season.
1. Choose a suitable
grouping and display
in a frequency table.
42 34 39 49 62 99 18 24 37 38
0
33 42 61 80 30 21
5
35
27 56 90
94 63 75 33 20 44 33 71
59 112 47 72 85 68 53 101 45 12
Runs
Tally
Frequency
0 - 19
20 - 39
Too many!
40 - 59
60 - 79
80 - 99
100 - 119
Too few!
Groups of
between 6 and
9 look best.
Drawing a Histogram from raw data.
The following data show the number of runs scored by an
opening batsman during matches last season.
1. Choose a suitable
grouping and display
in a frequency table.
42 34 39 49 62 99 18 24 37 38
0
33 42 61 80 30 21
5
35
27 56 90
94 63 75 33 20 44 33 71
59 112 47 72 85 68 53 101 45 12
Runs
Tally
Frequency
0 - 19
4
20 - 39
13
40 - 59
9
60 - 79
7
80 - 99
5
100 - 119
2
15
2. Complete the frequency table
then draw the histogram.
Runs scored in matches
10
f
5
0
0-19 20-39 40-59 60-79 80-99 100-119
Runs Scored
Comparing Histograms
Sixty students wrote two maths tests and their results are
recorded in the histogram below. The pass mark for both
tests was 30. Discuss the results for each set of tests.
25
Test 1 Scores
20
25
Test 2 Scores
20
15
f
10
15
f
5
5
10
0-9 10-19 20-29 30-39 40-49 50-60
Marks
0-9 10-19 20-29 30-39 40-49 50-60
Comparing
Marks
Drawing a Histogram from raw data.
The following data shows the height (as measured to the nearest cm)
of a random selection of cut flowers from Becky’s Flower Shop.
42 34 39 49 62 69 28 24 37 38
10
33 42 61 31 30
21 27 56 50
15
35 54 33 45 33
20 44 33 31
59 55
Height (h) in
cm
Tally
47 15 42 68
53 30 45 29
Frequency
Worksheet
Drawing a Histogram from raw data.
The following data shows the height (as measured to the nearest cm)
of a random selection of cut flowers from Becky’s Flower Shop.
1. Choose a suitable class
intervals and display in a
frequency table.
42 34 39 49 62 69 28 24 37 38
10
33 42 61 31 30
21 27 56 50
15
35 54 33 45 33
20 44 33 31
59 55
Height (h) in
cm
Tally
3
20  h < 30
6
30  h < 40
13
40  h < 50
8
50  h < 60
6
60  h < 70
4
53 30 45 29
2. Complete the frequency table
then draw the histogram.
Frequency
10  h < 20
47 15 42 68
15
Heights of Flowers
10
f
5
0
10
20
40
30
50
Height (cm)
60
70