AI generatedStatisticsGCSE Higher / IGCSE Extended

Finding a missing frequency-density scale

Finding a missing frequency-density scale.

  • Use a known class to calibrate the scale: density = frequency ÷ class width.
  • Divide its density by the number of vertical grid spaces to find the scale per space.
  • Frequency = width × density. Use each class’s own width; add frequencies to find total.

Example 1

The class has frequency 50. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk510152025300Frequency densityTime (minutes)
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 5 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency123456510152025300Frequency densityTime (minutes)

Example 2

The class has frequency 45. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk5101520253035400Frequency densityMass (g)
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 3 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency1234565101520253035400Frequency densityMass (g)

Your turn

Question 1

The class has frequency 40. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk10203040506070800Frequency densityLength (cm)
Check answer
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 1 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency2468101210203040506070800Frequency densityLength (cm)
Question 2

The class has frequency 20. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk5101520253035400Frequency densityTime (minutes)
Check answer
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 2 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency12345675101520253035400Frequency densityTime (minutes)
Question 3

The class has frequency 60. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk510152025300Frequency densityMass (g)
Check answer
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 6 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency1234567510152025300Frequency densityMass (g)
Question 4

The class has frequency 180. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk10203040506070800Frequency densityLength (cm)
Check answer
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 3 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency246810121410203040506070800Frequency densityLength (cm)
Question 5

The class has frequency 10. Find , the density at the first horizontal gridline above zero.

Histogram: bar area represents frequencyk5101520253035400Frequency densityTime (minutes)
Check answer
Known widthUse the class whose frequency is given.
Known densityFrequency ÷ width gives the actual height on the density scale.
The known bar spans 1 equal vertical grid spaces. Divide by that number.
Histogram: bar area represents frequency123456785101520253035400Frequency densityTime (minutes)
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