Which of the three averages is always an actual value from the data set?

The mode , since it is by definition the value that occurs most often. The mean and the median can both come out as numbers that never appear anywhere in the data.

What can you calculate from the mean that you cannot calculate from the mode?

The standard deviation and the skew , both of which are defined in terms of the mean. The mode leads to no measure of spread at all, which is one of its main weaknesses as an average.

What can the median be used to calculate?

The quartiles and the interquartile range , and it also appears in the formula for skew . That makes it a useful average to have even though it may not be one of the data values.

A grouped data set has an open-ended first class such as 'under 20'. Which average becomes unreliable, and which is unaffected?

The mean becomes unreliable, because an open-ended class has no midpoint to stand in for the values inside it. The modal class is unaffected, since finding it only needs to know which class has the highest frequency.

What is the mean's main advantage over the median?

It uses every value in the data set, so no information is thrown away. The median depends only on the middle position and takes no account of how far the other values lie from it.

Which measure of spread pairs with each average?

The pairings are: mode with the range , and only for quantitative data median with the interquartile range , or another range-type measure mean with the standard deviation

Which two pairings of average and spread should never be used?

Never pair the median with the standard deviation , which is defined in terms of the mean. Never pair the mean with the interquartile range , which is defined in terms of the quartiles.

You compare two data sets and state that one median is the higher. What else must your comparison include?

What that difference actually means in the context of the question, put in the question's own terms. Then the same again for a measure of spread: compare the two numbers, and say what the difference between them means.

Snails have a median of 7.1 cm and an interquartile range of 3.1 cm; slugs 9.7 cm and 4.5 cm. What two things does that tell you?

On average slugs travel further than snails, since their median is the higher of the two. The distances travelled by snails vary less, since their interquartile range is the smaller of the two.

Name two reasons a conclusion drawn from a data set might not be trustworthy.

The data set may be too small to represent the population, such as measuring only five pupils in a whole school. It may also be biased , such as measuring only the older year groups, which would push the average height up.

True or False? Two people presenting the same data will always reach the same conclusion.

False. Whoever presents the data chooses which average and which measure of spread to quote. Someone arguing a case might pick whichever average makes it look strongest, even though the underlying data has not changed at all.

What does a standardised score actually measure?

How many standard deviations the raw value lies away from the mean of its own data set. A positive score means the value sits above that mean, and a negative score means it sits below.

What does it mean for a distribution to have positive skew?

Its tail stretches out to the right , so most of the data sits at the lower end. Values above the median are more spread out than the values below it.

On a box plot, how can you tell the data has positive skew?

The median line sits closer to the lower quartile than to the upper one. In symbols, the median minus the lower quartile is smaller than the upper quartile minus the median.

Customer ages give a mean of 32.4, a median of 26 and a mode of 24. What does that suggest about the distribution?

Positive skew, since the mean is greater than the median, which is greater than the mode. Most of the customers are at the younger end, with a tail of older ones stretching upwards.

Which three quantities do you need in order to calculate a skew?

The mean , the median and the standard deviation . Skew compares how far apart the mean and the median are, measured against the spread of the data.

A skew value for a set of patient ages comes out as −1.12. What does that tell you?

The distribution is negatively skewed, because the value is negative. Most of the patients are at the older end, with a greater spread of ages below the median than above it.

True or False? A skew of −7 is a stronger skew than a skew of −3.

True. The further the skew value lies from zero, in either direction, the stronger the skew. A skew of exactly zero means the distribution is symmetrical.

GCSEStatisticsEdexcelHigherFlashcardsProcessing, Representing & Analysing DataUsing Summary Statistics

Using Summary Statistics (Edexcel GCSE Statistics: Higher): Flashcards

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FrontUsing Measures of Central Tendency
Which of the three averages is always an actual value from the data set?

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Cards in this collection (22)

Which of the three averages is always an actual value from the data set?
The mode, since it is by definition the value that occurs most often.
The mean and the median can both come out as numbers that never appear anywhere in the data.
What can you calculate from the mean that you cannot calculate from the mode?
The standard deviation and the skew, both of which are defined in terms of the mean.
The mode leads to no measure of spread at all, which is one of its main weaknesses as an average.
What can the median be used to calculate?
The quartiles and the interquartile range, and it also appears in the formula for skew.
That makes it a useful average to have even though it may not be one of the data values.
A grouped data set has an open-ended first class such as 'under 20'. Which average becomes unreliable, and which is unaffected?
The mean becomes unreliable, because an open-ended class has no midpoint to stand in for the values inside it.
The modal class is unaffected, since finding it only needs to know which class has the highest frequency.
Complete the rule about comparing two data sets.
When comparing two data sets you must use the $______$ average for both of them, and choose one that is $______$ for the context.
The completed rule is:
When comparing two data sets you must use the same average for both of them, and choose one that is appropriate for the context.
What is the mean's main advantage over the median?
It uses every value in the data set, so no information is thrown away.
The median depends only on the middle position and takes no account of how far the other values lie from it.
Which measure of spread pairs with each average?
The pairings are:
- mode with the range, and only for quantitative data
- median with the interquartile range, or another range-type measure
- mean with the standard deviation
Which two pairings of average and spread should never be used?
Never pair the median with the standard deviation, which is defined in terms of the mean.
Never pair the mean with the interquartile range, which is defined in terms of the quartiles.
You compare two data sets and state that one median is the higher. What else must your comparison include?
What that difference actually means in the context of the question, put in the question's own terms.
Then the same again for a measure of spread: compare the two numbers, and say what the difference between them means.
Snails have a median of 7.1 cm and an interquartile range of 3.1 cm; slugs 9.7 cm and 4.5 cm. What two things does that tell you?
On average slugs travel further than snails, since their median is the higher of the two.
The distances travelled by snails vary less, since their interquartile range is the smaller of the two.
Name two reasons a conclusion drawn from a data set might not be trustworthy.
The data set may be too small to represent the population, such as measuring only five pupils in a whole school.
It may also be biased, such as measuring only the older year groups, which would push the average height up.
True or False?
Two people presenting the same data will always reach the same conclusion.
False.
Whoever presents the data chooses which average and which measure of spread to quote.
Someone arguing a case might pick whichever average makes it look strongest, even though the underlying data has not changed at all.
Complete the formula for a standardised score.
$standardised score = \frac{______- μ}{______}$
The completed formula is:
$standardised score = \frac{x - μ}{σ}$
Here $x$ is the raw value, $μ$ is the mean and $σ$ is the standard deviation of that data set.
What does a standardised score actually measure?
How many standard deviations the raw value lies away from the mean of its own data set.
A positive score means the value sits above that mean, and a negative score means it sits below.
Michelle scores 80 in maths (mean 63.2, standard deviation 11.9) and 72 in English (mean 56.1, standard deviation 9.3). Which was the better performance?
English: her standardised scores are $\frac{80 - 63.2}{11.9} = 1.41$ in maths and $\frac{72 - 56.1}{9.3} = 1.71$ in English.
Her raw maths mark is the higher, but compared with everyone else who sat the papers she did better in English.
What does it mean for a distribution to have positive skew?
Its tail stretches out to the right, so most of the data sits at the lower end.
Values above the median are more spread out than the values below it.
On a box plot, how can you tell the data has positive skew?
The median line sits closer to the lower quartile than to the upper one.
In symbols, the median minus the lower quartile is smaller than the upper quartile minus the median.
Complete the ordering of the averages that suggests negative skew.
$mode______median______mean$
The completed ordering is:
$mode > median > mean$
In a perfectly symmetrical distribution all three averages are equal instead.
Customer ages give a mean of 32.4, a median of 26 and a mode of 24. What does that suggest about the distribution?
Positive skew, since the mean is greater than the median, which is greater than the mode.
Most of the customers are at the younger end, with a tail of older ones stretching upwards.
Which three quantities do you need in order to calculate a skew?
The mean, the median and the standard deviation.
Skew compares how far apart the mean and the median are, measured against the spread of the data.
A skew value for a set of patient ages comes out as −1.12. What does that tell you?
The distribution is negatively skewed, because the value is negative.
Most of the patients are at the older end, with a greater spread of ages below the median than above it.
True or False?
A skew of −7 is a stronger skew than a skew of −3.
True.
The further the skew value lies from zero, in either direction, the stronger the skew.
A skew of exactly zero means the distribution is symmetrical.

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