2. Histograms are similar to bar charts but there
are two main differences:
There are no gaps between the bars in a
histogram
The area of each bar is proportional to the
frequency that it represents. Hence, total area
is proportional to the total frequency.
The vertical axis is
labelled frequency
density.
frequency density = frequency divided by interval width
3. f = 15
f =4
f=6
frequency density = frequency divided by interval width
So, frequency = frequency density x interval width (area of the bars)
Frequencies = 1 x 6 = 6
= 3 x 5 = 15
= 2 x 2 = 4
4. frequency density = frequency divided by interval width
So, frequency = frequency density x interval width
5. Example 1
Display the following data as a histogram
Mass (g) 0-20 20-40 40-60 60-80 80-100
No of letters 10 18 24 14 18
6. Example 1
Display the following data as a histogram
Mass (g) 0-20 20-40 40-60 60-80 80-100
No of letters 10 18 24 14 18
solution
First find the intervals/ widths: NB the interval
widths don’t
For each one the width/ interval is 20
have to be the
same!
7. Example 1
Display the following data as a histogram
Mass (g) 0-20 20-40 40-60 60-80 80-100
No of letters 10 18 24 14 18
solution
First find the intervals/ widths:
For each one the width/ interval is 20
Then find the frequency density using frequency divided by interval/width
8. Example 1
Display the following data as a histogram
Mass (g) 0-20 20-40 40-60 60-80 80-100
No of letters 10 18 24 14 18
solution
First find the intervals/ widths:
For each one the width/ interval is 20
Then find the frequency density using frequency divided by interval/width
Mass (g) Interval Frequency Frequency density
width = frequency / width
0-20 20 10 0.5
20-40 20 18 0.9
40-60 20 24 1.2
60-80 20 14 0.7
80-100 20 18 0.9
9. Mass (g) Interval Frequency Frequency density
width = frequency / width
0-20 20 10 0.5
20-40 20 18 0.9
40-60 20 24 1.2
60-80 20 14 0.7
80-100 20 18 0.9
10. Finding frequencies from a histogram
To find a frequency in each interval use
frequency = interval width × frequency density
11. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Frequency density
Time late (mins)
12. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Minutes late Frequency density Frequency
= width x freq density
Frequency density
0-5
5-10
10-20
20-30
30-50
50-80
Time late (mins)
13. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Minutes late Frequency density Frequency
= width x freq density
Frequency density
0-5 6.4
5-10 8.8
10-20 3
20-30 1.2
30-50 0.6
50-80 0.2
Time late (mins)
14. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Minutes late Frequency density Frequency
= width x freq density
Frequency density
0-5 6.4 5 x 6.4
5-10 8.8 5 x 6.4
10-20 3 10 x 3
20-30 1.2 10 x 1.2
30-50 0.6 20 x 0.6
50-80 0.2 30 x 0.2
Time late (mins)
15. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Minutes late Frequency density Frequency
= width x freq density
Frequency density
0-5 6.4 5 x 6.4 = 32
5-10 8.8 5 x 6.4 =32
10-20 3 10 x 3 = 30
20-30 1.2 10 x 1.2 = 12
30-50 0.6 20 x 0.6 = 12
50-80 0.2 30 x 0.2 = 6
Time late (mins)
16. Example 2
A passengers' association conducted survey on punctuality of trains
using a particular station. The histogram shows the results.
•Construct the frequency distribution
•How many trains were there in the survey?
Minutes late Frequency density Frequency
= width x freq density
Frequency density
0-5 6.4 5 x 6.4 = 32
5-10 8.8 5 x 6.4 = 32
10-20 3 10 x 3 = 30
20-30 1.2 10 x 1.2 = 12
30-50 0.6 20 x 0.6 = 12
50-80 0.2 30 x 0.2 = 6
Time late (mins) Total trains =
32 + 32 + 30 + 12 + 12 + 6 =
17. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
Frequency Freq
density
0-10 50
10-20
20-25
25-30 20
30-50
Total 236
18. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20
5 20-25
25-30 20
30-50
Total 236
19. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25
25-30 20
30-50
Total 236
20. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25 76 15.2 x 5
25-30 20
30-50
Total 236
21. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25 76 15.2 x 5
25-30 20 20/5= 10
30-50
Total 236
22. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25 76 15.2 x 5
25-30 20 20/5= 10
30-50
Total 236
23. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 236 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25 76 15.2 x 5
25-30 20 20/5= 10
30-50 20 20/20 = 1
Total 236
24. 3. Abraham measured the time, in
seconds, that birds spent on each
individual visit to his bird table. The
birds made a total of 237 individual
visits.
The histogram shows some of the
15 results.
(a) Use the information in the histogram
to complete the frequency table
below.
(b) Use the table to complete the
histogram
10
Frequency Freq
density
0-10 50 50/ 10 = 5
10-20 70 7 x 10 = 70
5 20-25 76 15.2 x 5
25-30 20 20/5= 10
30-50 20 20/20 = 1
Total 236
