All you’ll ever need to know about histograms…

Success Criteria Grade Learning Outcome R A G C2 I can spot the differences between a bar chart and a histogram. C1 I know the difference between continuous and discrete data. B3 I can calculate frequency density from a grouped frequency table. B2 I can draw a histogram correctly, using the frequency density. B1 I can read a histogram, finding the actual number of people in a group using the frequency density. A3 I can draw conclusions from a histogram by performing calculations using information read from that histogram.

Spot The Difference Bar Chart Histogram Write down any differences you notice between the two graphs, including the bars, the axes and note down anything you aren’t sure about.

The Differences Bar Chart Histogram Category Property Bars X-Axis Y-Axis Category Property Bars X-Axis Y-Axis

The Differences Bar Chart Histogram Category Property Bars There are gaps between the bars. X-Axis Words or categories. (Discrete) Y-Axis Number of people or frequency. Category Property Bars There are no gaps between the bars and they are different widths. X-Axis Numbers. (Continuous) Y-Axis Frequency density – what’s that?

Discrete and Continuous Data – What’s The Difference? Discrete Data Continuous Data Discrete data can not be split up into “bits” – you either watched Eastenders or you didn’t. Continuous data can be split up – you can have 1.2 metres, 9.87 seconds or be 10.5 years old. Can you think of any examples of discrete data and continuous data?

Success Criteria Grade Learning Outcome R A G C2 I can spot the differences between a bar chart and a histogram. C1 I know the difference between continuous and discrete data. B3 I can calculate frequency density from a grouped frequency table. B2 I can draw a histogram correctly, using the frequency density. B1 I can read a histogram, finding the actual number of people in a group using the frequency density. A3 I can draw conclusions from a histogram by performing calculations using information read from that histogram.

Firstly, what does the group 0 ≤ h < 2 mean? It means: The group goes from 0 up to 2 hours, including 0 but not including 2. The group contains any value from 0 up to 1.99999999… hours.

Example Of How To Draw A Histogram: A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data. Hours (h) spent watching TV last week Frequency 0 ≤ h < 2 3 2 ≤ h < 5 6 5 ≤ h < 10 10 10 ≤ h < 20 25 20 ≤ h < 40 Why can’t we just plot the frequency?

How To Draw A Histogram: A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data. Hours (h) spent watching TV last week Frequency Frequency Density (Frequency ÷ Group Width) 0 ≤ h < 2 3 3 ÷ 2 = 1.5 2 ≤ h < 5 6 6 ÷ 3 = 2 5 ≤ h < 10 10 10 ÷ 5 = 2 10 ≤ h < 20 25 25 ÷ 10 = 2.5 20 ≤ h < 40 10 ÷ 20 = 0.5 Since the groups are all different widths we need to calculate the frequency density by dividing the frequency by the group width.

Drawing the histogram: Things to notice: The widths of the bars are the group widths. We plot the frequency density not the frequency.

Drawing the histogram: How could we calculate the frequency from the graph? Frequency = Freq. Density x Group Width Therefore the area of each bar is the frequency.

Histogram question: A survey of the heights of 100 Year 11 students was conducted with the results in the table below. Draw a histogram of this data. Height (x cm) Frequency 100 < x ≤ 120 20 120 < x ≤ 140 25 140 < x ≤ 150 150 < x ≤ 160 160 < x ≤ 200 10

Answer – first stage: Height (cm) Frequency Frequency Density 100 < x ≤ 120 20 20 ÷ 20 = 1 120 < x ≤ 140 25 25 ÷ 20 = 1.25 140 < x ≤ 150 25 ÷ 10 = 2.5 150 < x ≤ 160 20 ÷ 10 = 2 160 < x ≤ 200 10 10 ÷ 40 = 0.25

Answer – second stage: Height (cm) Frequency Frequency Density 100 < x ≤ 120 20 1 120 < x ≤ 140 25 1.25 140 < x ≤ 150 2.5 150 < x ≤ 160 2 160 < x ≤ 200 10 0.25

Success Criteria Grade Learning Outcome R A G C2 I can spot the differences between a bar chart and a histogram. C1 I know the difference between continuous and discrete data. B3 I can calculate frequency density from a grouped frequency table. B2 I can draw a histogram correctly, using the frequency density. B1 I can read a histogram, finding the actual number of people in a group using the frequency density. A3 I can draw conclusions from a histogram by performing calculations using information read from that histogram.

Reading Histograms Remember that frequency density is shown on the histogram. Frequency density = Frequency ÷ Group Width We discovered earlier that the area of each bar is the frequency.

Reading A Histogram This is a histogram of how many hours of TV some adults watched last week. How many adults were asked in total?

Draw yourself a table Hours (h) of TV watched Frequency Density

Draw yourself a table Answer: 34 Hours (h) of TV watched Frequency Density Frequency 0≤h<5 1 5 5≤h<10 2 10 10≤h<14 8 14≤h<20 6 20≤h<40 0.25 Answer: 34

Success Criteria Grade Learning Outcome R A G C2 I can spot the differences between a bar chart and a histogram. C1 I know the difference between continuous and discrete data. B3 I can calculate frequency density from a grouped frequency table. B2 I can draw a histogram correctly, using the frequency density. B1 I can read a histogram, finding the actual number of people in a group using the frequency density. A3 I can draw conclusions from a histogram by performing calculations using information read from that histogram.

Drawing Conclusions From Histograms What percentage of people in the survey below watched 20 hours or more of TV?

Calculate how many people are in each group: What do we do first? Calculate how many people are in each group:

Now find the percentage:

Success Criteria Grade Learning Outcome R A G C2 I can spot the differences between a bar chart and a histogram. C1 I know the difference between continuous and discrete data. B3 I can calculate frequency density from a grouped frequency table. B2 I can draw a histogram correctly, using the frequency density. B1 I can read a histogram, finding the actual number of people in a group using the frequency density. A3 I can draw conclusions from a histogram by performing calculations using information read from that histogram.