New
New
Lesson 9 of 11
New
New
- Year 11
Summary statistics from histograms
I can estimate the mean and median from a histogram.
Lesson details
Key learning points
- The mean can be found using a histogram
- The median can be found using a histogram
- An estimate for the frequency within a given data range can be found
Keywords
Arithmetic mean - The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
Frequency density - Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning that frequency density = frequency ÷ class width.
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.
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.
Statistics can be fun. A fun task is to collect the time it takes pupils to say the alphabet. Collect all the times using peer groups and represent in a histogram with equal class widths. Calculate the estimate mean from this data. Collect data from other Maths classes and compare estimate means.
Teacher tip
Licence
This content is © Oak National Academy Limited (2025), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).
Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.A __________ 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.
A __________ 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.
Correct answer: histogram
histogram
box plot
scatter diagram
pie chart
tally table
Q2.Here are the times taken to type the alphabet. Which of the following has a frequency density of 1.6?
Here are the times taken to type the alphabet. Which of the following has a frequency density of 1.6?
$$0 < t \leq 10$$
Correct answer: $$10 < t \leq 15$$
$$10 < t \leq 15$$
$$15 < t \leq 20$$
Correct answer: $$20 < t \leq 30$$
$$20 < t \leq 30$$
$$30 < t\leq 50$$
Q3.Here is some data on the lengths of some parcels. Which of the following have a frequency more than 13?
Here is some data on the lengths of some parcels. Which of the following have a frequency more than 13?
$$0 < l \leq 5$$
Correct answer: $$5 < l\leq 10$$
$$5 < l\leq 10$$
Correct answer: $$10 < l \leq 14$$
$$10 < l \leq 14$$
$$14< l \leq 16$$
Q4.Here is a histogram showing lengths of different fruit. $$x$$, $$y$$ and $$z$$ are what values?
Here is a histogram showing lengths of different fruit. $$x$$, $$y$$ and $$z$$ are what values?
$$x=1$$, $$y=2$$ and $$z=6$$
Correct answer: $$x=2$$, $$y=4$$ and $$z=6$$
$$x=2$$, $$y=4$$ and $$z=6$$
$$x=3$$, $$y=4$$ and $$z=5$$
$$x=4$$, $$y=8$$ and $$z=7$$
Q5.Here are the times taken to type the alphabet. Which of the following has a frequency greater than 10?
Here are the times taken to type the alphabet. Which of the following has a frequency greater than 10?
$$0 < t \leq 10$$
$$10 < t \leq 15$$
Correct answer: $$15 < t \leq 20$$
$$15 < t \leq 20$$
Correct answer: $$20 < t \leq 30$$
$$20 < t \leq 30$$
$$30 < t\leq 50$$
Q6.Here is a histogram showing the time it takes to solve a puzzle. What is the total frequency?
Here is a histogram showing the time it takes to solve a puzzle. What is the total frequency?
Correct Answer: 56
56
Assessment exit quiz
6 Questions
Q1.The (arithmetic) __________ for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
The (arithmetic) __________ for a set of numerical data is the sum of the values divided by the number of values. It is a measure of central tendency representing the average of the values.
Correct answer: mean
mean
median
mode
range
Q2.Histograms are excellent visual aids to show the distribution of data, but using the estimate mean from a histogram has more benefits. Select the appropriate reason.
Histograms are excellent visual aids to show the distribution of data, but using the estimate mean from a histogram has more benefits. Select the appropriate reason.
Correct answer: It provides statistical values for comparison.
It provides statistical values for comparison.
Visual representations of data are too vague.
Numbers are better than graphs.
Q3.Here are some times it takes for Oak class A to type the alphabet. Using the table, work out the estimate mean. There is no need to include the units.
Here are some times it takes for Oak class A to type the alphabet. Using the table, work out the estimate mean. There is no need to include the units.
Correct Answer: 16.85, 16.9, 17
16.85, 16.9, 17
Q4.Here are some times it takes for Oak class B to type the alphabet. Using the table, work out the estimate mean. There is no need to include the units.
Here are some times it takes for Oak class B to type the alphabet. Using the table, work out the estimate mean. There is no need to include the units.
Correct Answer: 13.75, 13.8, 14
13.75, 13.8, 14
Q5.The estimate mean for Oak class A was 16.85 seconds and the estimate mean for Oak class B was 13.75 seconds. What does this mean?
The estimate mean for Oak class A was 16.85 seconds and the estimate mean for Oak class B was 13.75 seconds. What does this mean?
Correct answer: Oak class B are quicker at typing the alphabet than Oak class A.
Oak class B are quicker at typing the alphabet than Oak class A.
Oak class A are quicker at typing the alphabet than Oak class B.
Both classes have the same estimate mean.
Oak class B are slower at typing the alphabet than Oak class A.
Correct answer: Oak class A are slower at typing the alphabet than Oak class B.
Oak class A are slower at typing the alphabet than Oak class B.
Q6.Work out the estimate median using this histogram showing lengths of pieces of wood. There is no need to include the units.
Work out the estimate median using this histogram showing lengths of pieces of wood. There is no need to include the units.
Correct Answer: 37.5
37.5
