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Year 8

Comparing summaries of data

I can use the different measures of central tendency and spread to compare two sets of data.

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New
New
Year 8

Comparing summaries of data

I can use the different measures of central tendency and spread to compare two sets of data.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Statistical summaries of data can be used to make inferences about that data.
  2. Two sets of statistical summaries can be used to compare the respective data sets.
  3. Statistical summaries have their limitations.

Common misconception

If two datasets have the same mean, then the distribution of data points will look similar.

Even with the same mean, two datasets could have vastly different ranges. One dataset could be bimodal, whilst the other could be unimodal.

Keywords

  • Central tendency - is a summary measure that attempts to describe a whole dataset with a single value that represents the middle or centre of its distribution.

  • Spread - The spread/dispersion of data values describes how far apart the pieces of data are.

  • Dispersion - The spread/dispersion of data values describes how far apart the pieces of data are.

Caution on the multi-use of the term "average". It is used: as an umbrella term for the mean, median, and mode; as well as to describe one average (most commonly the mean average); and as a general term to informally describe central tendency.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

Video

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Starter quiz

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6 Questions

Q1.
Which of these is not a measure of central tendency?
mean
median
mode
Correct answer: range
Q2.
Describe the modal properties of this data set: 12, 12, 9, 8, 8, 4, 0, 3, 12, 9, 9
mode at 12
mode at 9
bimodal at 12 and 8
Correct answer: bimodal at 12 and 9
trimodal at 8, 12, and 9
Q3.
By how much is the range of data set A greater than the range of data set B?
An image in a quiz
Correct Answer: 8, eight
Q4.
Match each of the mean, median, mode, and range to its value for this data set: 1, 1, 1, 3, 3, 5, 6, 7, 9
Correct Answer:mean,4

4

Correct Answer:median,3

3

Correct Answer:mode,1

1

Correct Answer:range,8

8

Q5.
Match each summary statistic to its value for this dot plot.
An image in a quiz
Correct Answer:range,9

9

Correct Answer:mode,10

10

Correct Answer:median,13

13

Q6.
Which of these is a reasonable estimate for the mean of this data set?
An image in a quiz
19
40
42.5
Correct answer: 50.8
58

Exit quiz

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6 Questions

Q1.
Match the summary statistic to the word that can be used to help in its interpretation.
Correct Answer:mean,typical value

typical value

Correct Answer:median,middle value

middle value

Correct Answer:mode,most frequent value

most frequent value

Correct Answer:range,how varied the data set is

how varied the data set is

Q2.
Which of these is a valid interpretation of the mean number of points Lucas and Sofia have scored when playing the new video game?
An image in a quiz
Both Lucas and Sofia's most frequent number of points per game is almost equal.
Sofia's typical number of points scored per game is lower than Lucas'.
Correct answer: Sofia's typical number of points scored per game is higher than Lucas'.
Lucas' middle-scoring game is lower than Sofia's middle-scoring game.
Lucas' middle-scoring game is higher than Sofia's middle-scoring game.
Q3.
Which of these is a valid interpretation of the range of points Lucas and Sofia scored when playing the new video game?
An image in a quiz
The variety of points Sofia scored is higher than Lucas'.
Correct answer: The variety of points Sofia scored is lower than Lucas'.
The variety of points Sofia and Lucas scored are almost equal.
Sofia has a lower consistency of points than Lucas.
Correct answer: Sofia has a higher consistency of points than Lucas.
Q4.
Which of these statements are true for the median and modal number of goals Jun and Aisha scored over 11 netball matches?
An image in a quiz
The median number of goals scored by Jun in a match is higher than Aisha.
Correct answer: The median number of goals scored by Aisha in a match is higher than Jun.
The modal number of goals scored in a match by Aisha and Jun are equal.
Correct answer: Aisha's goals scored in a match is bimodal, with one mode higher than Jun's.
Q5.
Which of these statements are an accurate interpretation of the number of goals Jun and Aisha scored over 11 netball matches?
An image in a quiz
On a mean average match, Jun will score 2 goals more than Aisha.
Correct answer: On a mean average match, Jun and Aisha will score the same number of goals.
Correct answer: However, Aisha is more consistent at scoring goals.
However, Jun is more consistent at scoring goals.
Q6.
Which of these statements combine to make an accurate comparison of which class performed better on an end-of-topic quiz.
An image in a quiz
The typical score of a student in class A is 1.6 higher than class B.
Correct answer: The typical score of a student in class B is 1.6 higher than class A.
Correct answer: However, class A had a more consistent set of scores.
Correct answer: In conclusion, class B did better, as their middle-scoring student did better.
In conclusion, class A did better, as their most frequent score was higher.