Moving between tables and histograms | Maths | Quizalize & Oak National Academy

Starter quiz

Frequency density is proportional to the frequency per unit for the data in each class. Often, the multiplier is 1 meaning...

Frequency density = frequency $\times$ class width

Frequency density = frequency $\div$ class width ✓

Frequency density = class width $\div$ frequency
Select which statements are true.

Histograms can show discrete and continuous data. ✓

Histograms show the distribution of data using grouped intervals. ✓

Histograms with unequal bar widths must be plotted against frequency density. ✓

Histograms with unequal bar widths must be plotted against frequency.

Histograms with equal bar widths must not be plotted against frequency density.
Here is some data on the masses of parcels. Which class interval shows a frequency density of 2?

$0 < w \leq 5$

$5 < w \leq 15$ ✓

$15 < w \leq 30$
Here is some data on the lengths of some string. Which class interval shows a frequency density of 1.4?

$0 < l \leq 15$

$15 < l \leq 20$

$20 < l \leq 30$ ✓

$30 < l \leq 35$
The histogram shows the masses of different parcels. How many parcels have a mass between 5 and 15 kg?

'20' ✓
Select which of the following statements are true given a histogram with unequal bar widths plotted against frequency density.

The highest bar shows the modal class.

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 smallest bar area shows the smallest frequency. ✓

Exit quiz

Which of the following shows the frequency in a histogram with unequal bar widths?

The area of the bar ✓

The height of the bar

The length of the bar

The frequency density
Here are the times taken to type the alphabet. Match the class intervals with the correct frequency density.

$0 < t \leq 10$

⇔

Frequency density = 0.4 ✓

$10 < t \leq 15$

⇔

Frequency density = 1.6 ✓

$15 < t \leq 20$

⇔

Frequency density = 4 ✓

$30 < t\leq 50$

⇔

Frequency density = 0.25 ✓
Here is some data on the lengths of some parcels. Match the frequency with the class interval.

$0 < l \leq 5$

⇔

12 ✓

$5 < l \leq 10$

⇔

15 ✓

$10 < l \leq 14$

⇔

20 ✓

$15< l \leq 16$

⇔

4 ✓
Here is a histogram showing lengths of different fruit. Which numbers represent $x$ , $y$ and $z$ on the $y$ axis?

$x=1$ , $y=2$ and $z=5$

$x=2$ , $y=4$ 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. Match the class interval to the correct frequency.

$0 < t \leq 10$

⇔

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 ✓
Here is a histogram showing the time it takes to solve a puzzle.

$0 < t\leq 2$

⇔

Frequency = 10 ✓

$2 < t \leq 4$

⇔

Frequency density = 6 ✓

$4 < t \leq 5$

⇔

Frequency = 15 ✓

$5 < t\leq 10$

⇔

Frequency density = 2.8 ✓

$10 < t \leq 12$

⇔

Frequency density = 2.5 ✓

Worksheet

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Video

Lesson Details

Key learning points

A frequency table can be used to construct a histogram
A histogram can be used to construct a frequency table
Data is sometimes collected using uneven class widths

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

Continuous data - Continuous data can take any value within a range. (Height, mass, temperature)
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.
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.