Summarising data | Maths | Quizalize & Oak National Academy

Starter quiz

Match the summary statistic to its definition.
- mean
  
  ⇔
  
  is the sum of the values divided by the number of values ✓
- median
  
  ⇔
  
  is the middle piece of data when the data are in order ✓
- mode
  
  ⇔
  
  is the most frequent value ✓
- range
  
  ⇔
  
  is a measure of spread ✓
Find the mode of this list of numbers: 4, 7, 16, 16, 22, 23, 24, 28
- 7
- 16 ✓
- 17.5
- 19
- 24
Find the median of this list of numbers. 4, 7, 16, 16, 22, 23, 24, 28
- 7
- 16
- 17.5
- 19 ✓
- 24
Find the modal value of this dataset from its dot plot.
- 9
- 11
- 28
- 29 ✓
- 30
Work out the mean of this dataset: (-6), (-5), (-3), (-3), 1, 4, 5, 7
- '0' ✓
Dataset A and dataset B both show the minimum temperatures in two different locations. How much bigger is the range of dataset A than the range of dataset B?
- '11' ✓

Exit quiz

Which of these most closely describe a "measure of central tendency"?
- A single value that summarises how spread out or varied a dataset is
- Always a single value that calculates the middle number in an ordered dataset
- Usually a single value that calculates the middle number in an ordered dataset
- Always a single value representing a central property of a distribution
- Usually a single value representing a central property of a distribution ✓
Describe the modal properties of this dataset: 2, 2, 6, 5, 6, 6, 3, 4, 0, 9, 2
- mode at 2
- mode at 6
- bimodal at 2 and 5
- bimodal at 2 and 6 ✓
- trimodal at 2, 5, and 6
For the following dataset, match the summary statistic to its value: 10, 14, 14, 18, 19, 21, 23
- mean
  
  ⇔
  
  17 ✓
- median
  
  ⇔
  
  18 ✓
- mode
  
  ⇔
  
  14 ✓
- range
  
  ⇔
  
  13 ✓
Which of these is the most likely value of the mean for this dataset, represented by a dot plot?
- 10
- 76
- 80 ✓
- 86
- 90
In which of these dot plots would the mode be a representative summary of the dataset?
- a
- b ✓
- c
- d ✓
Which of the following statements are true for this dot plot when evaluating whether the median is a representative summary of the data?
- The median is approximately 21. ✓
- The median is approximately 17 and 26.
- The median may not be the most representative summary. ✓
- The median will never be a useful summary for this dataset.
- The median can still be a useful summary for this dataset. ✓

Worksheet

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Lesson Details

Key learning points

The mode is a useful measure of central tendency for certain data sets.
The median is a useful measure of central tendency for certain data sets.
The mean is a useful measure of central tendency for certain data sets.

Common misconception

The mean is the most meaningful average.

Looking at bimodal data, trimodal data or data with extreme outliers. Context may be relevant.

Keywords

Data - Data are a collection of information.
Mean - The (arithmetic) mean for a set of numerical data is the sum of the values divided by the number of values.
Median - The median is the central (middle) piece of data when the data are in numerical order.
Mode - Mode is the most frequent value. It is a measure of central tendency representing the average of the values.
Measure of central tendency - A summary that attempts to describe a whole set of data with a single value that represents the middle of the distribution.