StudyBrixFree worksheets, study guides and courses

Mathematics · Grades 6–10

Data interpretation and misleading summaries

Check the axis, units, scale, population and sample size.

Make a worksheet

Understand the idea

Read the full display

Check the axis, units, scale, population and sample size.

Choose the summary

Mean, median and range describe different features.

Limit the claim

An association alone does not identify a cause.

Worked examples

Find the median of 2, 3, 3, 5 and 17.

The middle value in the ordered list is 3.

3

Find the mean of 2, 3, 3, 5 and 17.

The sum is 30; 30/5 = 6.

6

Try it yourself

  1. Which change can exaggerate differences in bar heights?

    1. Labelling the units
    2. Stating the sample size
    3. Using equally spaced tick marks
    4. Starting the vertical axis well above zero without clear context

  2. Why might the median better describe a typical value when one measurement is extremely high?

  3. A survey has 80 responses, including 28 choosing cycling. What percentage chose cycling?

  4. Which sample is most likely to overrepresent regular library users?

    1. A random sample from the whole community list
    2. A sample selected independently of library visits
    3. A randomly selected sample of households
    4. People interviewed as they leave the library

Answers and marking notes

Answers and marking notes
  1. Starting the vertical axis well above zero without clear context

    A truncated scale can make small changes look large.

  2. The extreme value pulls the mean more strongly; the median depends on order and the central position.

    Credit recognition that suitability depends on the question, not a universal rule.

  3. 35

    28/80 × 100 = 35%.

  4. People interviewed as they leave the library

    The collection location selects people who already visit.

Preview material · independent educational review required. Grade bands are approximate, not official curriculum alignment.