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MathidiaMathematics Academy
Data collection and representation
Lesson 44 of 75
Challenge

Representing distributions

Objective. Choose and interpret histograms, box plots and cumulative frequency.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Representing distributions means choosing an appropriate diagram to display and interpret data, with histograms showing frequency density for grouped continuous data, box plots summarising five key statistics (minimum, lower quartile, median, upper quartile, maximum), and cumulative frequency graphs showing running totals used to estimate medians and quartiles. A histogram's bar height equals frequency density = frequency ÷ class width, not frequency itself, which matters for unequal class widths. For example, a box plot quickly reveals skewness: if the median is closer to the lower quartile than the upper quartile, the data is positively skewed. Choosing the right representation depends on what feature of the distribution, such as spread, skewness, or shape, needs to be shown clearly.

Worked example

A histogram bar for the class 10–25 has a frequency density of 4. Use this to find the frequency represented by this bar in the data representation.

10254
Bar chart of the values 10, 25, 4
  1. 1Recall frequency density = frequency ÷ class width.
  2. 2Find the class width: 25 − 10 = 15.
  3. 3Rearrange: frequency = frequency density × class width.
  4. 4Compute: frequency = 4 × 15 = 60.

Answer: 60

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Practice

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Common mistake. Students often plot raw frequency as the height of histogram bars even when class widths differ, distorting the shape of the distribution. Always calculate frequency density (frequency ÷ class width) as the bar height whenever class widths are unequal.

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