# Problem solving with cumulative frequency and histograms

I can use my knowledge of cumulative frequency and histograms to solve problems.

# Problem solving with cumulative frequency and histograms

I can use my knowledge of cumulative frequency and histograms to solve problems.

## Lesson details

### Key learning points

- Different representations of the same data set give a fuller picture
- It is important to identify what features are used to analyse a data set
- It is important to identify what features are used to compare two data sets

### 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

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

Lower quartile - 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).

Upper quartile - 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).

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.

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Video

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## Starter quiz

### 6 Questions

$$0 < t \leq 10$$ -

Frequency = 4

$$10 < t \leq 15$$ -

Frequency = 8

$$15 < t \leq 20$$ -

Frequency = 20

$$20 < t \leq 30$$ -

Frequency = 16

$$30 < t\leq 50$$ -

Frequency = 5

$$0 < t\leq 2$$ -

10

$$2 < t \leq 4$$ -

12

$$4 < t \leq 5$$ -

15

$$5 < t\leq 10$$ -

14

$$10 < t \leq 12$$ -

5

## Exit quiz

### 6 Questions

A boxplot -

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

A histogram -

a diagram with rectangles whose area is proportional to the frequency

Lower quartile -

the value under which 25% of data points are found

Upper quartile -

the value under which 75% of data points are foun

Class C -

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

Class B -

is on average the lowest performing class

Class A and B -

have the same IQR and range

Class A and C -

have on average the higher performing students