Summary statistics from histograms | Maths | Quizalize & Oak National Academy

Starter quiz

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.

histogram ✓

box plot

scatter diagram

pie chart

tally table
Here are the times taken to type the alphabet. Which of the following has a frequency density of 1.6?

$0 < t \leq 10$

$10 < t \leq 15$ ✓

$15 < t \leq 20$

$20 < t \leq 30$ ✓

$30 < t\leq 50$
Here is some data on the lengths of some parcels. Which of the following have a frequency more than 13?

$0 < l \leq 5$

$5 < l\leq 10$ ✓

$10 < l \leq 14$ ✓

$14< l \leq 16$
Here is a histogram showing lengths of different fruit. $x$ , $y$ and $z$ are what values?

$x=1$ , $y=2$ and $z=6$

$x=2$ , $y=4$ and $z=6$ ✓

$x=3$ , $y=4$ and $z=5$

$x=4$ , $y=8$ and $z=7$
Here are the times taken to type the alphabet. Which of the following has a frequency greater than 10?

$0 < t \leq 10$

$10 < t \leq 15$

$15 < t \leq 20$ ✓

$20 < t \leq 30$ ✓

$30 < t\leq 50$
Here is a histogram showing the time it takes to solve a puzzle. What is the total frequency?

'56' ✓

Exit quiz

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.

mean ✓

median

mode

range
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.

It provides statistical values for comparison. ✓

Visual representations of data are too vague.

Numbers are better than graphs.
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.

'16.85' ✓
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.

'13.75' ✓
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?

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.

Oak class A are slower at typing the alphabet than Oak class B. ✓
Work out the estimate median using this histogram showing lengths of pieces of wood. There is no need to include the units.

'37.5' ✓

Worksheet

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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

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

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.