What is discrete data?

Discrete data refers to data that can only take certain numerical values . It is often (but not always) data that can be counted . Examples of discrete data include: Number of pets Shoe size Number of petals on a flower

What is continuous data?

Continuous data refers to data that can take any numerical value within a range . It is usually data that needs to be measured . Examples of continuous data include: Height Weight Time taken to complete a jigsaw

How do you find the mean of a set of numbers?

To find the mean of a set of numbers: Add the values together. Divide by the total number of values.

How do you find the median of a set of numbers?

To find the median of a set of numbers: Put the numbers in order . Find the middle number. If there are two middle numbers then the median is the midpoint of those numbers.

How do you find the mode of a set of numbers?

The mode of a set of numbers is the value that appears the most .

True or False? There can be more than one median value in a data set.

False. There can not be more than one median value in a data set. The median is the middle value . The only average that can have more than one value is the mode .

True or false? The mean is affected by extreme values .

True. The mean is affected by extreme values .

True or false? The median is affected by extreme values .

False. The median is not affected by extreme values .

Define the range of a set of data.

The range is the difference between the highest value and the lowest value. It measures how spread out the data is, and it is not a kind of average.

True or False? A data set with a larger range must have a larger average.

False. The range describes only how spread out the values are, not where they sit. Two data sets can share the same average while one of them is far more spread out than the other.

Define the lower quartile and the upper quartile .

The lower quartile is the value a quarter of the way along the data when it is in order, so a quarter of the values lie below it. The upper quartile is the value three quarters of the way along, with three quarters of the values below it.

When you split ordered data into a lower half and an upper half to find the quartiles, what happens to the median?

With an odd number of values the median is left out of both halves, and with an even number every value goes into one half or the other. An even number of values has no single middle value to leave out, because the median falls between two of them.

Why can the interquartile range describe the spread of a data set better than the range can?

Because the interquartile range covers only the middle 50% of the data, so it is not affected by extreme values . Discarding the bottom quarter and the top quarter removes exactly the values that would otherwise stretch a measure of spread.

How do you find the mode from a frequency table ?

To find the mode from a frequency table , look for the value with the highest frequency .

For grouped data , which average from the calculator can you rely on?

The mean is the one to take from the calculator. It still displays a median and quartiles, but after every value has been replaced by its class midpoint those are not dependable estimates of the real ones.

True or False? When entering a plain list of raw data, the calculator's frequency setting should be 1.

True. Each value in the list occurs once , so a frequency of 1 counts every entry exactly once. If the frequency is left pointing at another column the calculator will weight the values and return the wrong averages.

A calculator is given the data 43, 29, 70, 51, 64, 43. What are the median and the two quartiles ?

The median is 47 , the lower quartile is 43 and the upper quartile is 64 for this data. Sorting the six values gives 29, 43, 43, 51, 64, 70, which is a quick way to check the display has been read correctly.

How can you describe a data set with a smaller range than another?

Its values are closer together , more consistent , or show less variation . All three phrases describe the same thing, so any one of them will do.

When writing a comparison, how should you word the part that explains what the numbers mean?

Use the exact wording of the question , naming the two groups and the quantity being measured. A sentence phrased in the context, such as one class performing better than another, says more than a statement about which number is bigger.

True or False? A smaller range is always the better result.

False. Whether a small spread is desirable depends entirely on the context . A teacher may want marks bunched together, while an examiner may want them spread out so that grade boundaries are clearer.

Why might a conclusion drawn from two data sets not be reliable?

The samples may be too small to represent the whole population, or they may be biased . Measuring only five pupils in a school, or only the older year groups, would give a misleading picture.

How can the person presenting a comparison influence its conclusion?

They can choose whichever average best supports the argument they want to make. The mean, median and mode can point in different directions for the same data, so the choice itself carries an opinion.

IGCSEMathsCambridge (CIE)International MathsCoreFlashcardsStatisticsAverages, Ranges & Comparing Data

Averages, Ranges & Comparing Data (Cambridge (CIE) IGCSE International Maths: Core): Flashcards

Exam code: 0607

1/37

0Still learning

Know0

FrontDiscrete & Continuous Data
What is discrete data?
BackDiscrete & Continuous Data
Discrete data refers to data that can only take certain numerical values. It is often (but not always) data that can be counted.
Examples of discrete data include:
Number of pets
Shoe size
Number of petals on a flower
BackDiscrete & Continuous Data
Sign up to unlock flashcards
Join for free to unlock a full flashcard set, track what you know,
and turn revision into real progress.
FrontDiscrete & Continuous Data
What is continuous data?
BackDiscrete & Continuous Data
Continuous data refers to data that can take any numerical value within a range. It is usually data that needs to be measured.
Examples of continuous data include:
Height
Weight
Time taken to complete a jigsaw
FrontMean, Median & Mode
How do you find the mean of a set of numbers?
BackMean, Median & Mode
To find the mean of a set of numbers:
Add the values together.
Divide by the total number of values.

Was this flashcard helpful?

Cards in this collection (37)

What is discrete data?
Discrete data refers to data that can only take certain numerical values. It is often (but not always) data that can be counted.
Examples of discrete data include:
- Number of pets
- Shoe size
- Number of petals on a flower
What is continuous data?
Continuous data refers to data that can take any numerical value within a range. It is usually data that needs to be measured.
Examples of continuous data include:
- Height
- Weight
- Time taken to complete a jigsaw
How do you find the mean of a set of numbers?
To find the mean of a set of numbers:
1. Add the values together.
2. Divide by the total number of values.
How do you find the median of a set of numbers?
To find the median of a set of numbers:
1. Put the numbers in order.
2. Find the middle number.
If there are two middle numbers then the median is the midpoint of those numbers.
How do you find the mode of a set of numbers?
The mode of a set of numbers is the value that appears the most.
True or False?
There can be more than one median value in a data set.
False.
There can not be more than one median value in a data set. The median is the middle value.
The only average that can have more than one value is the mode.
True or false?
The mean is affected by extreme values.
True.
The mean is affected by extreme values.
True or false?
The median is affected by extreme values.
False.
The median is not affected by extreme values.
How can you find the total of all data values if you know the mean and the number of values?
E.g. if the mean of a set of 25 values is 3.7, what is the total of all values in the data set?
If you know the mean and number of values, you can calculate the total of values by rearranging the mean formula:
- $total of values = mean \times number of values$
E.g. if the mean of a set of 25 values is 3.7, then the total of all values in the data set is $3.7 \times 25 = 92.5$ .
How can you find the number of data values if you know the mean and the total of the values?
E.g. if the total of a set of data values is 66 and the mean is 8.25, how many data values are there?
If you know the mean and total of the data values, you can calculate the number of values by rearranging the mean formula:
- $number of values = \frac{total of values}{mean}$
E.g. the total number of data values in a set of data with a total of 66 and mean of 8.25 is $\frac{66}{8.25} = 8$ .
How can you find the new mean of a data set if a new data item is added to the set?
E.g. a data set of 12 items has a mean of 5.7.
A new data item of 9.6 is added to the set.
What is the new mean?
To find the new mean of a data set if a new data item is added to the set:
1. Find the total of the current data set: $total of values = mean \times number of values$
2. Add the new data item
3. Divide by the new total number of data items
E.g. for a data set of 12 items and a mean of 5.7, the total of the values is $12 \times 5.7 = 68.4$ .
Therefore when a new data item of 9.6 is added to the set, the new mean is $\frac{68.4 + 9.6}{13} = 6$ .
Define the range of a set of data.
The range is the difference between the highest value and the lowest value.
It measures how spread out the data is, and it is not a kind of average.
Complete the working for the range of $- 2$ , $- 1$ , $0$ and $4$ :
$4 - (- 2) =______$
The completed working is:
$4 - (- 2) = 6$
Subtracting a negative lowest value adds it on, so the range is larger than the highest value by itself.
Why is the range a poor measure of spread for the data 1, 2, 5, 80?
The range is $80 - 1 = 79$ , which is distorted by the single extreme value.
Most of the data lies between 1 and 5, so 79 describes the outlier rather than the data set.
A data set has a highest value of 9.2 and a lowest value of 2.8. Find the range.
The range is 6.4, since $9.2 - 2.8 = 6.4$ .
Write the subtraction out rather than only the answer, so that the method is visible.
True or False?
A data set with a larger range must have a larger average.
False.
The range describes only how spread out the values are, not where they sit.
Two data sets can share the same average while one of them is far more spread out than the other.
Define the lower quartile and the upper quartile.
The lower quartile is the value a quarter of the way along the data when it is in order, so a quarter of the values lie below it.
The upper quartile is the value three quarters of the way along, with three quarters of the values below it.
When you split ordered data into a lower half and an upper half to find the quartiles, what happens to the median?
With an odd number of values the median is left out of both halves, and with an even number every value goes into one half or the other.
An even number of values has no single middle value to leave out, because the median falls between two of them.
Fill in the two gaps to complete the rule for the interquartile range.
The interquartile range is found by subtracting the $______$ quartile from the $______$ quartile.
The completed rule is:
The interquartile range is found by subtracting the lower quartile from the upper quartile.
As a formula this is $IQR = UQ - LQ$ , and because the upper quartile is never the smaller of the two the answer is never negative.
Find the lower quartile, the upper quartile and the interquartile range of 3, 5, 8, 9, 12, 15, 20.
The lower quartile is 5, the upper quartile is 15, and the interquartile range is $15 - 5 = 10$ .
The lower half is 3, 5, 8 and the upper half is 12, 15, 20, and the middle value of each half gives that half's quartile.
True or False?
The median of a data set is also its second quartile.
True.
The quartiles divide ordered data into four equal parts, and the median is the middle one of the three dividing values.
That is why it is sometimes written $Q_{2}$ , with the lower and upper quartiles written $Q_{1}$ and $Q_{3}$ .
Why can the interquartile range describe the spread of a data set better than the range can?
Because the interquartile range covers only the middle 50% of the data, so it is not affected by extreme values.
Discarding the bottom quarter and the top quarter removes exactly the values that would otherwise stretch a measure of spread.
How do you find the mean from a frequency table?
To find the mean from a frequency table:
1. Include a column for (value $\times$ frequency).
2. Add the values in this column.
3. Divide the sum by the total frequency.
How do you find the median from a frequency table?
To find the median from a frequency table:
1. Make sure the values in the table are in order.
2. Find the $\frac{n + 1}{2}$ th value, where $n$ is the total frequency.
How do you find the mode from a frequency table?
To find the mode from a frequency table, look for the value with the highest frequency.
Which averages does the one-variable statistics function on a graphic display calculator give you?
It gives the mean, written $\bar{x}$ on most models, together with the median and the lower and upper quartiles.
The quartiles usually appear as $Q_{1}$ and $Q_{3}$ on the display.
Complete the rule for entering a frequency table into a graphic display calculator.
Put the data item in the first column and its $______$ in the second column, then tell the calculator which column is which.
The completed rule is:
Put the data item in the first column and its frequency in the second column, then tell the calculator which column is which.
Without that second column the calculator would treat every value as occurring just once.
Why can grouped data not be entered into a calculator exactly as it is given?
A calculator needs a single number for each data item, and a class such as $5 < l \leq 10$ is a range rather than one value.
You therefore assume every item in a class sits at the class midpoint, and enter that instead.
For grouped data, which average from the calculator can you rely on?
The mean is the one to take from the calculator.
It still displays a median and quartiles, but after every value has been replaced by its class midpoint those are not dependable estimates of the real ones.
True or False?
When entering a plain list of raw data, the calculator's frequency setting should be 1.
True.
Each value in the list occurs once, so a frequency of 1 counts every entry exactly once.
If the frequency is left pointing at another column the calculator will weight the values and return the wrong averages.
A calculator is given the data 43, 29, 70, 51, 64, 43. What are the median and the two quartiles?
The median is 47, the lower quartile is 43 and the upper quartile is 64 for this data.
Sorting the six values gives 29, 43, 43, 51, 64, 70, which is a quick way to check the display has been read correctly.
True or False?
A calculator mean of $26.07142 \dots$ minutes should be written down in full.
False.
Round it to 3 significant figures, giving 26.1 minutes as the answer.
Answers that are not exact should be given to at least 3 significant figures, unless the question asks for a different accuracy.
How can you describe a data set with a smaller range than another?
Its values are closer together, more consistent, or show less variation.
All three phrases describe the same thing, so any one of them will do.
When writing a comparison, how should you word the part that explains what the numbers mean?
Use the exact wording of the question, naming the two groups and the quantity being measured.
A sentence phrased in the context, such as one class performing better than another, says more than a statement about which number is bigger.
True or False?
A smaller range is always the better result.
False.
Whether a small spread is desirable depends entirely on the context.
A teacher may want marks bunched together, while an examiner may want them spread out so that grade boundaries are clearer.
Why might a conclusion drawn from two data sets not be reliable?
The samples may be too small to represent the whole population, or they may be biased.
Measuring only five pupils in a school, or only the older year groups, would give a misleading picture.
How can the person presenting a comparison influence its conclusion?
They can choose whichever average best supports the argument they want to make.
The mean, median and mode can point in different directions for the same data, so the choice itself carries an opinion.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:Probability Diagrams & Multiple EventsNext:Statistical Diagrams