Histograms with equal bar width | Maths | Quizalize & Oak National Academy

Starter quiz

The ______ of the box on a box plot represents the interquartile range.

'width' ✓
What is the interquartile range of the data represented on this box plot?

'19 cm' ✓
Calculate the interquartile range from this cumulative frequency graph.

'6' ✓
What is the interquartile range of this set of data? 17, 13, 19, 21, 13, 14, 19.

'6' ✓
This table shows information about the heights of some year 7 and 11 pupils. Compare their heights by selecting the most useful response.

The Y11 median and interquartile range are both higher than Y7.

The Y11 median was higher, but the interquartile range is lower than Y7.

On average, Y11 are taller and their heights are more consistent. ✓

On average, Y11 are taller and their heights are less consistent.
This table shows information about the times some children and adults take to complete a puzzle. Compare their times by selecting the most useful response.

The adults' median was lower and their interquartile range was higher.

On average the adults did better but their times are less consistent. ✓

The children's median was better and their interquartile range was lower.

On average the adults did better and their times are more consistent.

On average the children did better and their times are less consistent.

Exit quiz

Select the examples of continuous data.

50 people were asked how many books they read a week.

50 people were asked how many minutes it takes them to get to work/school. ✓

50 people were asked what their favourite fruit is.

50 pieces of fruit were weighed. ✓
When constructing a histogram with equal bar widths, select which of the following are important points to remember.

Axis scale increasing equally. ✓

Equal bar width with the $y$ axis labelled frequency. ✓

Equal gap widths between each bar.

The $x$ and $y$ axis must have the same scale.
Here is a table showing how long people watched TV for in a week. Select the correct statements which match this table.

12 people spent between 4 and 5 hours watching TV. ✓

12 people spent between 0 and 1 hour watching TV.

22 people spent between 1 and 3 hours watching TV. ✓

28 people spent between 3 and 5 hours watching TV.
Here is a histogram showing times taken to complete an IQ test. Select the correct statements which match this chart.

It took 5 people between 0 and 2 minutes to complete the IQ test. ✓

It took 7 people between 4 and 6 minutes to complete the IQ test. ✓

It took 23 people between 4 and 10 minutes to complete the IQ test.

It took 2 people between 18 and 20 minutes to complete the IQ test.

50 people took the IQ test. ✓
Here is a histogram showing the times people played a game until they first lost a life. What percentage of people played for 20 seconds or fewer?

'40%' ✓
Here is a histogram showing the times people played a game until they first lost a life.

20

⇔

Total number of people who took part ✓

2

⇔

Number of people who lost a life within 10 seconds of starting ✓

8

⇔

Number of people who played for more than half a minute ✓

19

⇔

The number of people who lost a life within 40 seconds of starting ✓

95

⇔

Percentage of people who lost a life within 40 seconds of playing ✓

Worksheet

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Presentation

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Video

Lesson Details

Key learning points

A histogram is a bar chart for continuous data
The bars are adjacent due to the nature of the data
The bars are all the same width to allow easier comparisons

Common misconception

Histograms with unequal bar widths are plotted against the frequency and/or pupils read the frequency density as the frequency of the class width.

Show what a histogram with unequal bar widths looks like when plotted against frequency. This visual aid will show pupils the distribution of data is difficult to see.

Keywords

Histogram - A histogram is a diagram consisting of rectangles whose area is proportional to the frequency in each class and whose width is equal to the class interval.