A box plot is a diagram that clearly shows the minimum and maximum value of a data set long with the three quartiles.

The lower quartile is the value under which 25% of data points are found when they are arranged in increasing order.  Also known as the first quartile (Q1).

The upper quartile is the value under which 75% of data points are found when they are arranged in increasing order.  Also known as the third quartile (Q3).

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.

Problem solving with cumulative frequency and histograms

Maths

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.

Graphical representations of data: cumulative frequency and histograms

a diagram that clearly shows the min and max values and the quartiles

a diagram with rectangles whose area is proportional to the frequency

the value under which 25% of data points are found

the value under which 75% of data points are foun

50% of Class A scores were more consistent with the median than Class B.

50% of Class B scores were more consistent with the median than Class A.

Here are some test scores for Class A and Class B. Select the statement which is true.

Here are two box plots showing the scores of two classes. Select the statements which are true.

Here are three different cumulative frequency graphs showing different classes' test percentages. The scale is unlabelled but is the same for all graphs. Which class has the lowest average score

has the most consistent scores as the IQR and range is the smallest

is on average the lowest performing class

have on average the higher performing students

Here are three box plots showing different classes' test percentages. The scale is unlabelled but is the same for all graphs. 

Here are some masses of sweets in a bag. 50% of the sweets are ≤ 120 g but greater than 80 g. What percentage are greater than 120 g but less than or equal to 180 g?

The bar with the largest area shows the modal class.

The frequency is the frequency density $$\div$$ class width.

The lowest bar shows the class width with the lowest frequency.

The highest bar shows the class width with the highest frequency.

Which of the following is true for a histogram with unequal bar widths?

Here are the times taken to type the alphabet. Match the class width with its frequency.

Here is a histogram showing the time it takes to solve a puzzle. Match the class width with its frequency.

Which class' scores were more consistent?

Calculate the interquartile range from this cumulative frequency graph.

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

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

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

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

The adults median was better and their interquartile range was lower.

This table show information about the times taken by some children and adults to complete a puzzle.  Compare their times.  Which is the correct response to this question?

This lesson will be removed by end of Summer Term 2025.

Problem solving with cumulative frequency and histograms

Lesson outcome

This lesson will be removed by end of Summer Term 2025.