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Cumulative Frequency 2

Maths: Edexcel IGCSE Higher, topic 6.2.4

Cumulative Frequency Analysis

Cumulative frequency diagrams can be used to estimate different important values in a set of data such as the median, quartiles and inter-quartile range.

Estimation not calculation

Estimation not calculation

  • Cumulative frequency diagrams can be used to estimate values.
  • Cumulative frequency diagrams CANNOT be used to work out accurate values.
The median piece of data

The median piece of data

  • You can find which person is the middle piece of data using the equation above.
  • You can then use this to find the value of the median piece of data.
Median from cumulative frequency

Median from cumulative frequency

  • The median of a set of data can be estimated by drawing a line from the middle piece of data on your cumulative frequency diagram on the y-axis until it hits the curve.
  • Then draw a vertical line down to the x-axis.
  • The number on the x-axis is an estimate for the median.

Cumulative Frequency Analysis

Cumulative frequency diagrams can be used to estimate different important values in a set of data such as the median, quartiles and inter-quartile range.

Quartiles

Quartiles

  • A set of data can be split into four quartiles.
  • Each quartile includes 14\large\frac{1}{4} of the pieces of data in the data set.
  • The values 14\large\frac{1}{4}, 24\large\frac{2}{4} and 34\large\frac{3}{4} of the way through a set of data are known as Q1, Q2 and Q3 respectively.
Calculating the quartiles

Calculating the quartiles

  • Quartiles can be calculated in a similar way to the median.
  • Start by finding the median value (this is the same as Q2).
  • Then find the median of the bottom half of the data smaller than Q2 (this is Q1).
  • Then find the median of the top half of the data larger than Q2 (this is Q3).
Interquartile range

Interquartile range

  • The interquartile range is a measure of how spread out the data is.
  • You calculate the interquartile range by working out Q3 − Q1.

Test yourself on Cumulative Frequency 2

  • What time did the median person enter Glastonbury Festival?

  • What is the equation to find the median piece of data from a set of data?

  • What time did the median person pay for a ticket?

  • Which of these is the formula for the interquartile range?

  • What is the interquartile range of the following quartiles?
    Q1 = 4
    Q2 = 16
    Q3 = 18

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