Rukasha Maths

GCSE maths Beta

Histograms and frequency density · Revision guide

Higher · Statistics · 1 page in the PDF

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Learning objectives

  • Calculate frequency density for unequal class widths.
  • Recover frequency from a histogram bar area.

Key ideas

Use the class boundaries to find each width.

class width=upper boundary−lower boundary\text{class width}=\text{upper boundary}-\text{lower boundary}

Divide frequency by class width to calculate the bar height.

frequency density=frequencyclass width\text{frequency density}=\frac{\text{frequency}}{\text{class width}}

Multiply density by width to recover frequency.

frequency=density×class width\text{frequency}=\text{density}\times\text{class width}

Histogram bar area represents frequency. Adjoining bars can have unequal widths.

Worked examples

Example 1

Times are grouped in intervals from zero to ten, ten to thirty and thirty to fifty, with frequencies 8, 30 and 12. Find their densities.

0≤t<10,10≤t<30,30≤t<500\le t<10,\quad10\le t<30,\quad30\le t<50
class widths:10, 20, 20\text{class widths}:10,\ 20,\ 20
densities:810, 3020, 1220\text{densities}:\frac8{10},\ \frac{30}{20},\ \frac{12}{20}
0.8,1.5,0.60.8,\quad1.5,\quad0.6

Example 2

A class has width eight and frequency twenty-four. Find its density.

density=248\text{density}=\frac{24}{8}
33

Watch out

Bar height is density, not frequency. Equal heights can represent different frequencies when class widths differ.