An outlier is an extreme data value that does not fit the general pattern of the data. Outliers arise in two quite different ways, and telling them apart is what decides what you do next: from a genuine but unusual event, such as one very high salary in a company from a mistake in collecting or recording the data, such as a test score above 100%

An outlier has been identified in a data set. Should it be removed?

Not automatically: look at the context to work out where it came from. If it is an error , remove it: a test score of over 100% cannot be real, so it is a mistake in the data collection. If it is a genuine value, keep it: a salary far above the others is probably the chief executive's, and it is part of the data.

Define cleaning data .

Cleaning data is removing the values that should not be analysed: errors , and missing data. Outliers that turn out to be mistakes are cleaned out this way, but cleaning is wider than outliers alone: a value can be an obvious error without being extreme, and a blank entry is neither. What cleaning must never be is removing an awkward value that is genuine, since that misrepresents the data.

True or False? If two outliers are found in a data set, both should be cleaned out of it.

False. Each outlier is judged separately, on where it came from. So, for example , in a list of the ages of children at a birthday party, the values 13 and 29 are both flagged as outliers, and the 29 is clearly an error, since a 29 year old is not a child. The 13 is unusual but perfectly possible, so it should be investigated rather than deleted.

When you describe or compare data sets, which two kinds of statistic must you always give?

A measure of location , such as the mean or the median, and a measure of spread , such as the range, the interquartile range or the standard deviation. One without the other is incomplete: the location says where the data sits, the spread says how consistent or how varied it is, and two data sets with the same average can look completely different. A smaller measure of spread means the data is more consistent , and a larger one means it is more varied.

Which measure of spread goes with the mean, and which goes with the median?

The mean is paired with the standard deviation or the variance, and the median with the interquartile range or the range. They pair up because the mean and the standard deviation both use every value in the data set, while the median and the interquartile range are both based on position, so each pair reacts to an extreme value in the same way. Mixing a pair, such as quoting the median alongside the standard deviation, is what loses marks in a comparison.

True or False? Adding a new data value that is below the mean will make the mean decrease.

True. The mean is calculated from every value, so a value below it pulls it down; equally, removing a value from above the mean makes the mean decrease, and the two opposite cases make it increase. The median and quartiles behave much less predictably: they may move or stay exactly where they are, depending on whereabouts in the ordered data the new value falls, so they have to be checked case by case. An extreme value shifts the mean a long way, but affects the median no more than any other value would.

Does a lower mean always describe the better performance?

No: it depends entirely on what is being measured. A lower mean is better for the time taken to complete a puzzle, and worse for a score on a test. This is why a comparison must be written in the context of the data, not as a statement about the numbers: one mean being smaller says nothing until you say what it means for the situation.

A LevelMathsEdexcelStatisticsFlashcardsData Presentation & InterpretationWorking with Data

Working with Data (Edexcel A Level Maths: Statistics): Flashcards

Exam code: 9MA0

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FrontOutliers & Cleaning Data
Define outlier.
BackOutliers & Cleaning Data
An outlier is an extreme data value that does not fit the general pattern of the data.
Outliers arise in two quite different ways, and telling them apart is what decides what you do next:
from a genuine but unusual event, such as one very high salary in a company
from a mistake in collecting or recording the data, such as a test score above 100%
BackOutliers & Cleaning Data
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Cards in this collection (11)

Define outlier.
An outlier is an extreme data value that does not fit the general pattern of the data.
Outliers arise in two quite different ways, and telling them apart is what decides what you do next:
- from a genuine but unusual event, such as one very high salary in a company
- from a mistake in collecting or recording the data, such as a test score above 100%
What are the two rules used to decide whether a data value counts as an outlier?
Both rules set a boundary a stated distance out from the middle of the data.
Measured from the quartiles, a value is an outlier if it is less than $Q_{1} - k \times IQR$ or greater than $Q_{3} + k \times IQR$ , most commonly with $k = 1.5$ .
Measured from the mean, a value is an outlier if it is less than $\bar{x} - k σ$ or greater than $\bar{x} + k σ$ , most commonly with $k = 2$ .
A data set has $Q_{1} = 4$ and $Q_{3} = 7.5$ , and an outlier is defined as a value more than $1.5 \times$ the interquartile range beyond a quartile. Complete the upper boundary:
$7.5 + 1.5 \times______=______$
The completed calculation is:
$7.5 + 1.5 \times 3.5 = 12.75$
The interquartile range has to be worked out first, from $7.5 - 4 = 3.5$ , since the rule is stated in terms of the IQR rather than the quartiles themselves.
Any value above 12.75 is an outlier. Work out the lower boundary too, from $4 - 1.5 \times 3.5 = - 1.25$ : here that is below every possible value, so there are no outliers at the bottom end.
An outlier has been identified in a data set. Should it be removed?
Not automatically: look at the context to work out where it came from.
If it is an error, remove it: a test score of over 100% cannot be real, so it is a mistake in the data collection.
If it is a genuine value, keep it: a salary far above the others is probably the chief executive's, and it is part of the data.
Define cleaning data.
Cleaning data is removing the values that should not be analysed: errors, and missing data.
Outliers that turn out to be mistakes are cleaned out this way, but cleaning is wider than outliers alone: a value can be an obvious error without being extreme, and a blank entry is neither.
What cleaning must never be is removing an awkward value that is genuine, since that misrepresents the data.
True or False?
If two outliers are found in a data set, both should be cleaned out of it.
False.
Each outlier is judged separately, on where it came from.
So, for example, in a list of the ages of children at a birthday party, the values 13 and 29 are both flagged as outliers, and the 29 is clearly an error, since a 29 year old is not a child.
The 13 is unusual but perfectly possible, so it should be investigated rather than deleted.
When you describe or compare data sets, which two kinds of statistic must you always give?
A measure of location, such as the mean or the median, and a measure of spread, such as the range, the interquartile range or the standard deviation.
One without the other is incomplete: the location says where the data sits, the spread says how consistent or how varied it is, and two data sets with the same average can look completely different.
A smaller measure of spread means the data is more consistent, and a larger one means it is more varied.
Which measure of spread goes with the mean, and which goes with the median?
The mean is paired with the standard deviation or the variance, and the median with the interquartile range or the range.
They pair up because the mean and the standard deviation both use every value in the data set, while the median and the interquartile range are both based on position, so each pair reacts to an extreme value in the same way.
Mixing a pair, such as quoting the median alongside the standard deviation, is what loses marks in a comparison.
Complete the rule for choosing which pair of statistics to use:
Use the mean and standard deviation when the data is roughly $______$ and contains no outliers.
Use the median and interquartile range when the data contains $______$ .
The completed rule is:
Use the mean and standard deviation when the data is roughly symmetrical and contains no outliers.
Use the median and interquartile range when the data contains outliers.
Extreme values that are not going to be cleaned out pull the mean towards themselves and inflate the standard deviation, which makes both unreliable as a description of the data. The median and interquartile range are barely moved by them.
True or False?
Adding a new data value that is below the mean will make the mean decrease.
True.
The mean is calculated from every value, so a value below it pulls it down; equally, removing a value from above the mean makes the mean decrease, and the two opposite cases make it increase.
The median and quartiles behave much less predictably: they may move or stay exactly where they are, depending on whereabouts in the ordered data the new value falls, so they have to be checked case by case.
An extreme value shifts the mean a long way, but affects the median no more than any other value would.
Does a lower mean always describe the better performance?
No: it depends entirely on what is being measured.
A lower mean is better for the time taken to complete a puzzle, and worse for a score on a test.
This is why a comparison must be written in the context of the data, not as a statement about the numbers: one mean being smaller says nothing until you say what it means for the situation.

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