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Year 8

Changing a data point

I can see how certain statistical measures may change as a result of changes in the data.

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New
New
Year 8

Changing a data point

I can see how certain statistical measures may change as a result of changes in the data.

Download all resources
Share activities with pupils

Lesson details

Key learning points

  1. Changing the value of one data point can affect the mode.
  2. Changing the value of one data point can affect the median.
  3. Changing the value of one data point can affect the mean.

Common misconception

Averages (mean, median, mode) will always change if a data point needs to be added, removed, edited.

The mean, median, or mode will remain invariant if a data point is added with the same value as that average.

Keywords

  • Bimodal - Sets of data which have two modes are known as bimodal data.

  • 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 a set of numerical data is in numerical order.

  • Mode - The mode is the most frequent value in a dataset.

In the world of statistics, data that has been collected cannot just be modified to change its summaries. The only time a dataset can be changed is if new data is collected, data becomes outdated, or recording errors are found.
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).

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Starter quiz

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6 Questions

Q1.
Which of these statements defines the median?
The most frequent value when the data are put into numerical order.
The distance on a number line between the smallest and largest data point.
The sum of values divided by the number of values in a data set.
Correct answer: The middle piece of data when the data are put into numerical order.
Q2.
Calculate the mean for this data set.
An image in a quiz
7
16
Correct answer: 17.5
19
24
Q3.
Match the summary statistic to its value.
An image in a quiz
Correct Answer:mean,3

3

Correct Answer:median,4

4

Correct Answer:mode,-1

-1

Correct Answer:range,12

12

Q4.
Which of these statements is true for this dot plot?
An image in a quiz
The data set has a single mode.
Correct answer: The data set is bimodal.
Correct answer: The mode does not appear to be the most representative summary.
Because the mode is not representative, it is not a useful summary.
Correct answer: Even though the mode isn't representative, this information can still be useful.
Q5.
First calculate the mean for this dot plot, then select the correct statements.
An image in a quiz
Correct answer: The mean is 10.
The mean is 19.
The mean is representative because many data points share the same value.
Correct answer: The mean isn't very representative because not many data point are close to it.
The mean isn't very representative because the range is bigger.
Q6.
Without carrying out any calculations select which of these statements are likely to be true for this dot plot.
An image in a quiz
The median is 13.
The median is 78.
Correct answer: The median is 83.
The median is close to the two peaks of high frequency values in the data set.
Correct answer: The median is in the dip of low or no frequency values in the data set.

Exit quiz

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6 Questions

Q1.
One data point on this dot plot was incorrectly typed in. After the data point is modified and corrected, Andeep notices the mode has changed. Which of these statements must be true?
An image in a quiz
Correct answer: The incorrect data point is 14.
The incorrect data point is 16.
The incorrect data point is 20.
The data paint must be corrected to 14.
Correct answer: The data point must be corrected to 16.
Q2.
The mean of this dot plot is currently 15.75. A new data point is collected and added to the data set. Laura re-calculates the mean and notices it has decreased. What could the new data point be?
An image in a quiz
Correct answer: 9
Correct answer: 15
15.75
16
22
Q3.
The mean of this dot plot is 15.75. A data point is no longer relevant and removed from the data set. Sam re-calculates the mean and notices it has decreased. What could the new data point be?
An image in a quiz
9
15
15.75
Correct answer: 16
Correct answer: 22
Q4.
A data point is removed from this dataset, as it is no longer relevant to an investigation. Which of the following are possible outcomes after the data point is removed?
An image in a quiz
The data set may become bimodal.
Correct answer: The mode of the data set may stay the same.
The mode of the data set may change to a different value.
Correct answer: There may be no mode in the data set.
Q5.
Match each possible change to the data set to the correct description of its impact on the median.
An image in a quiz
Correct Answer:A data point of 2 is added,The median becomes 4.

The median becomes 4.

Correct Answer:A data point of 4 is removed,The median becomes 9.

The median becomes 9.

Correct Answer:A data point of 6.5 is added,The median stays the same.

The median stays the same.

Correct Answer:4 is modified in value to a 7,The median becomes 8.

The median becomes 8.

Q6.
Match each possible change to the data set to the correct description of its impact on the mean.
An image in a quiz
Correct Answer:4 is modified in value to a 20,The mean increases by 2.

The mean increases by 2.

Correct Answer:9 is modified in value to a 1,The mean decreases by 1.

The mean decreases by 1.

Correct Answer:A data point of 20 is added,The mean increases to 8.

The mean increases to 8.

Correct Answer:A data point of 6.5 is added,The mean stays the same.

The mean stays the same.

Correct Answer:All the 9s are removed,The mean decreases to 4.

The mean decreases to 4.