1. Histograms All you’ll ever need to know about histograms…

2. Success Criteria Learning OutcomeRAG I can spot the differences between a bar chart and a histogram. I know the difference between continuous and discrete data. I can calculate frequency density from a grouped frequency table. I can draw a histogram correctly, using the frequency density. I can read a histogram, finding the actual number of people in a group using the frequency density. I can draw conclusions from a histogram by performing calculations using information read from that histogram.

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

4. The Differences Bar Chart CategoryProperty Bars X-Axis Y-Axis Histogram CategoryProperty Bars X-Axis Y-Axis

5. The Differences Bar Chart CategoryProperty BarsThere are gaps between the bars. X-AxisWords or categories. (Discrete) Y-AxisNumber of people or frequency. Histogram CategoryProperty BarsThere are no gaps between the bars and they are different widths. X-AxisNumbers. (Continuous) Y-AxisFrequency density – what’s that?

6. Discrete and Continuous Data – What’s The Difference? Discrete DataContinuous Data Discrete data can not be split up into “bits”. For example, the number of students in a class. 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?

7. Success Criteria Learning OutcomeRAG I can spot the differences between a bar chart and a histogram. I know the difference between continuous and discrete data. I can calculate frequency density from a grouped frequency table. I can draw a histogram correctly, using the frequency density. I can read a histogram, finding the actual number of people in a group using the frequency density. I can draw conclusions from a histogram by performing calculations using information read from that histogram.

8. 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.

9. Example Of How To Draw A Histogram: Hours (h) spent watching TV last week Frequency 0 ≤ h < 23 2 ≤ h < 56 5 ≤ h < 1010 10 ≤ h < 2025 20 ≤ h < 4010 A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data. Why can’t we just plot the frequency?

10. How To Draw A Histogram: Hours (h) spent watching TV last week Frequency Frequency Density (Frequency ÷ Group Width) 0 ≤ h < 233 ÷ 2 = 1.5 2 ≤ h < 566 ÷ 3 = 2 5 ≤ h < 101010 ÷ 5 = 2 10 ≤ h < 202525 ÷ 10 = 2.5 20 ≤ h < 401010 ÷ 20 = 0.5 A survey has been conducted on how many hours of TV some children watched last week. Draw a histogram for this data. Since the groups are all different widths we need to calculate the frequency density by dividing the frequency by the group width.

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

12. 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.

13. Histogram question: Height (x cm)Frequency 100 < x ≤ 12020 120 < x ≤ 14025 140 < x ≤ 15025 150 < x ≤ 16020 160 < x ≤ 20010 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.

14. Answer – first stage: Height (cm)FrequencyFrequency Density 100 < x ≤ 1202020 ÷ 20 = 1 120 < x ≤ 1402525 ÷ 20 = 1.25 140 < x ≤ 1502525 ÷ 10 = 2.5 150 < x ≤ 1602020 ÷ 10 = 2 160 < x ≤ 2001010 ÷ 40 = 0.25

15. Answer – second stage: Height (cm)Frequency Frequency Density 100 < x ≤ 120201 120 < x ≤ 140251.25 140 < x ≤ 150252.5 150 < x ≤ 160202 160 < x ≤ 200100.25

16. Success Criteria GradeLearning OutcomeRAG I can spot the differences between a bar chart and a histogram. I know the difference between continuous and discrete data. I can calculate frequency density from a grouped frequency table. I can draw a histogram correctly, using the frequency density. I can read a histogram, finding the actual number of people in a group using the frequency density. I can draw conclusions from a histogram by performing calculations using information read from that histogram.