BTEOTSSSBAT draw and interpret histograms

Histograms

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

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

f = 6

f = 15

f =4

frequency density = frequency divided by interval width

So, frequency = frequency density x interval width

Mass (g) 0-20 20-40 40-60 60-80 80-100

No of letters 10 18 24 14 18

Example 1Display 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

Example 1Display the following data as a histogram

solutionFirst find the intervals/ widths: For each one the width/ interval is 20

NB the interval widths don’t have to be the same!

Mass (g) 0-20 20-40 40-60 60-80 80-100

No of letters 10 18 24 14 18

Example 1Display the following data as a histogram

solutionFirst find the intervals/ widths: For each one the width/ interval is 20Then find the frequency density using frequency divided by interval/width

Mass (g) 0-20 20-40 40-60 60-80 80-100

No of letters 10 18 24 14 18

Example 1Display the following data as a histogram

solutionFirst find the intervals/ widths: For each one the width/ interval is 20Then find the frequency density using frequency divided by interval/width

Mass (g) Interval width

Frequency Frequency density= 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

Mass (g) Interval width

Frequency Frequency density= 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

Finding frequencies from a histogram

To find a frequency in each interval use

frequency = interval width × frequency density

Example 2A 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?

Time late (mins)

Freq

uenc

y de

nsity

Example 2A 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

0-5

5-10

10-20

20-30

30-50

50-80

Time late (mins)

Freq

uenc

y de

nsity

Example 2A 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

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)

Freq

uenc

y de

nsity

Example 2A 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

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)

Freq

uenc

y de

nsity

Example 2A 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

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)

Freq

uenc

y de

nsity

Example 2A 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

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)

Freq

uenc

y de

nsity

Total trains =32 + 32 + 30 + 12 + 12 + 6 =

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

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

5

Frequency Freq density

0-10 50 50/ 10 = 5

10-20

20-25

25-30 20

30-50

Total 236

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

5

10

15

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25

25-30 20

30-50

Total 236

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

5

10

15

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25 76 15.2 x 5

25-30 20

30-50

Total 236

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25 76 15.2 x 5

25-30 20 20/5= 10

30-50

Total 236

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

5

10

15

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25 76 15.2 x 5

25-30 20 20/5= 10

30-50

Total 236

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

5

10

15

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25 76 15.2 x 5

25-30 20 20/5= 10

30-50 20 20/20 = 1

Total 236

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

5

10

15

Frequency Freq density

0-10 50 50/ 10 = 5

10-20 70 7 x 10 = 70

20-25 76 15.2 x 5

25-30 20 20/5= 10

30-50 20 20/20 = 1

Total 236

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 results.(a) Use the information in the histogram

to complete the frequency table below.

(b) Use the table to complete the histogram

5

10

15