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 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.

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.

Summary statistics from histograms

Maths

Constructing a cumulative frequency graph

Interpreting a cumulative frequency graph

Constructing box plots

Comparing box plots

Interquartile range

Histograms with equal bar width

Histograms with unequal bar width

Moving between tables and histograms

Constructing histograms and box plots using technology

Problem solving with cumulative frequency and histograms

In the prior unit, pupils compared two different sets of data. In this unit, pupils consider cumulative frequency graphs and histograms and compare these with other known graphical representations.

In this unit, pupils consider cumulative frequency graphs and histograms, and compare these with other known graphical representations.

Graphical representations of data: cumulative frequency and histograms

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.

It provides statistical values for comparison.

Visual representations of data are too vague.

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.

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 B to type the alphabet. Using the table, work out the estimate mean. There is no need to include the units.

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.

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?

Work out the estimate median using this histogram showing lengths of pieces of wood. There is no need to include the units.

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.

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

Here is some data on the lengths of some parcels. Which of the following have a frequency more than 13?

Here is a histogram showing lengths of different fruit. $$x$$, $$y$$ and $$z$$ are what values?

Here are the times taken to type the alphabet. Which of the following has a frequency greater than 10?

Here is a histogram showing the time it takes to solve a puzzle. What is the total frequency?

Summary statistics from histograms

Lesson outcome