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 .

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 .

Why can you only estimate the mean from grouped data?

Because the original data values are lost once they have been grouped, so there is no way to find their exact total. The estimate assumes instead that every value in a class is equal to that class's midpoint .

True or False? From a grouped frequency table you can work out the exact value of the median.

False. You can only find the class interval containing the median, not the median itself, because the individual values are unknown. Work out the position of the median first, then read down a running total of the frequencies to see which interval that position falls in.

Define the range of a data set.

The range is the highest value minus the lowest value . It measures how spread out the data is, and it is not an average.

True or False? The range tells you a typical value in the data set.

False. The range measures spread , not a typical value, so it says nothing about where the data sits. Two data sets can share the same range and still have completely different averages.

Why can one unusually large value change the range a great deal?

Because the range uses only the highest and lowest values and ignores everything in between. A single extreme value becomes one of those two, so it sets the range almost on its own.

What kind of data does a bar chart show, and what goes on each axis?

It shows discrete data, which can be counted, whether numerical like shoe sizes or categorical like colours of cars. The horizontal axis carries the different outcomes and the vertical axis carries the frequency.

How do you read the mode off a bar chart?

The mode is the outcome with the tallest bar . Give that outcome itself as your answer, not the height of the bar.

True or False? A dual bar chart is used to compare two different data sets.

True. It puts the bars in pairs , side by side, for each outcome. That lets the two sets be read against each other outcome by outcome, instead of on two separate charts.

How do you find the total number of items represented by one set of bars on a bar chart?

Add together the heights of all the bars in that set, since each height is a frequency. On a dual bar chart, add only the bars belonging to the set you have been asked about.

How do you find the median from data shown in a bar chart?

Turn the chart back into a frequency table first, reading each bar's height as its frequency. Then find the median from that table in the usual way.

A pie chart is drawn for a set of data where the total frequency is 180 . What do you do to the frequency of each item to find its angle for the pie chart?

If a pie chart is drawn for a set of data where the total frequency is 180 , you multiply the frequency of an item by 2 (i.e. 360 ÷ 180) to find the size of its angle on the pie chart.

In a pie chart, if you know that the angle 30° represents a frequency of 10 , how would you find the total frequency ?

In a pie chart, if an angle of 30° represents a frequency of 10, then you can find the total frequency by: dividing 10 by 30 to find how much 1° represents, then multiplying this by 360. Alternatively, you can see how many times 30° goes into 360° and then multiply this by 10.

How do you calculate the angles needed for a pie chart ?

To calculate the angles needed for a pie chart: Divide each frequency by the total frequency. Multiply each result by 360°. Alternatively: Divide 360° by the total frequency. Multiply each frequency by this number.

If you are given the angles in a pie chart and the total frequency , how do you calculate the individual frequencies ?

If you are given the angles in a pie chart and the total frequency , you can calculate the individual frequencies by doing the following: Divide each angle by 360°. Multiply by the total frequency. Alternatively: Divide the total frequency by 360. Multiply each angle by this number.

What sorts of things should you look for when reading and interpreting statistical diagrams ?

When reading and interpreting statistical diagrams , you should look for: Keys Shading Axis labels The word "frequency" Any unusual or unexpected information mentioned

Define anomaly in the context of statistical diagrams.

An anomaly , otherwise known as an extreme value or outlier, is a data point that is significantly different from the rest of the data.

True or false? You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect .

True. You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect , such as uneven gaps in axis values or a missing key.

Define key in the context of statistical diagrams.

In the context of statistical diagrams, a key is a legend that explains the meaning of symbols, colours, or shading used in the diagram.

True or False? The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages , spread , and unusual data values for the data sets represented by the diagrams.

True. The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages , spread , and unusual data values for the data sets represented by the diagrams.

What should you consider when deciding which measures to compare in statistical diagrams?

When deciding which measures to compare in statistical diagrams, you should consider: Whether the mean, median or mode is the appropriate average to use. Whether the range or interquartile range is the appropriate measure of spread to use. Whether any assumptions or potential issues with the data could affect the reliability of the results and comparisons.

True or false? You should aim to make at least one pair of comments when comparing statistical diagrams.

False. You should aim to make at least two pairs of comments when comparing statistical diagrams: One pair should compare averages and comment on what this means in the context of the question. The other pair should compare spread and comment on what this means in the context of the question.

IGCSEMathsEdexcelMaths BFlashcardsStatistics & ProbabilityStatistics Toolkit

Statistics Toolkit (Edexcel IGCSE Maths B): Flashcards

Exam code: 4MB1

1/42

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 (42)

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 $\frac{68.4 + 9.6}{13} = 6$ .
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.
Why can you only estimate the mean from grouped data?
Because the original data values are lost once they have been grouped, so there is no way to find their exact total.
The estimate assumes instead that every value in a class is equal to that class's midpoint.
What is the midpoint of the class interval $150 \leq x < 160$ ?
It is $155$ , found by adding the two endpoints and dividing by 2.
So the midpoint is $\frac{150 + 160}{2} = \frac{310}{2} = 155$ .
Fill in the two missing words.
An estimate of the mean from grouped data is the total of the $______$ times frequency column, divided by the total $______$ of the data.
The completed sentence is:
An estimate of the mean from grouped data is the total of the midpoint times frequency column, divided by the total frequency of the data.
Those products are usually written in an extra column headed $f x$ , and that column is the one you total.
What do you give as your answer when asked for the modal class?
The class interval with the highest frequency, written out in full.
If the highest frequency is 34 against the interval $40 \leq x < 50$ , the modal class is $40 \leq x < 50$ , not 34.
True or False?
From a grouped frequency table you can work out the exact value of the median.
False.
You can only find the class interval containing the median, not the median itself, because the individual values are unknown.
Work out the position of the median first, then read down a running total of the frequencies to see which interval that position falls in.
A grouped table has frequencies 2, 4, 6, 5, 2 and 1 in order. Which interval contains the median?
The total frequency is 20, so the median lies at the $\frac{20 + 1}{2} = 10.5$ th value.
The running totals are 2, 6, 12, 17, 19 and 20, so the 10.5th value falls in the third interval.
Define the range of a data set.
The range is the highest value minus the lowest value.
It measures how spread out the data is, and it is not an average.
What is the range of $- 2$ , $- 1$ , $0$ and $4$ ?
It is $6$ , because $4 - (- 2) = 4 + 2 = 6$ .
Subtracting a negative lowest value adds it on, which is where this calculation most often goes wrong.
True or False?
The range tells you a typical value in the data set.
False.
The range measures spread, not a typical value, so it says nothing about where the data sits.
Two data sets can share the same range and still have completely different averages.
Why can one unusually large value change the range a great deal?
Because the range uses only the highest and lowest values and ignores everything in between.
A single extreme value becomes one of those two, so it sets the range almost on its own.
Four numbers written in order are $w$ , $9$ , $x$ and $22$ , and their range is 19. What is $w$ ?
Because the numbers are in order, $w$ is the lowest and $22$ is the highest, so $22 - w = 19$ .
Rearranging gives $w = 3$ .
What kind of data does a bar chart show, and what goes on each axis?
It shows discrete data, which can be counted, whether numerical like shoe sizes or categorical like colours of cars.
The horizontal axis carries the different outcomes and the vertical axis carries the frequency.
Fill in the two missing words about drawing a bar chart.
The bars must be separated by $______$ and they must all have the same $______$ as each other.
The completed sentence is:
The bars must be separated by gaps and they must all have the same width as each other.
It is the heights of the bars that show the frequencies, so equal widths are what keep the comparison fair.
How do you read the mode off a bar chart?
The mode is the outcome with the tallest bar.
Give that outcome itself as your answer, not the height of the bar.
True or False?
A dual bar chart is used to compare two different data sets.
True.
It puts the bars in pairs, side by side, for each outcome.
That lets the two sets be read against each other outcome by outcome, instead of on two separate charts.
How do you find the total number of items represented by one set of bars on a bar chart?
Add together the heights of all the bars in that set, since each height is a frequency.
On a dual bar chart, add only the bars belonging to the set you have been asked about.
How do you find the median from data shown in a bar chart?
Turn the chart back into a frequency table first, reading each bar's height as its frequency.
Then find the median from that table in the usual way.
A pie chart is drawn for a set of data where the total frequency is 180.
What do you do to the frequency of each item to find its angle for the pie chart?
If a pie chart is drawn for a set of data where the total frequency is 180, you multiply the frequency of an item by 2 (i.e. 360 ÷ 180) to find the size of its angle on the pie chart.
In a pie chart, if you know that the angle 30° represents a frequency of 10, how would you find the total frequency?
In a pie chart, if an angle of 30° represents a frequency of 10, then you can find the total frequency by:
- dividing 10 by 30 to find how much 1° represents,
- then multiplying this by 360.
Alternatively, you can see how many times 30° goes into 360° and then multiply this by 10.
How do you calculate the angles needed for a pie chart?
To calculate the angles needed for a pie chart:
- Divide each frequency by the total frequency.
- Multiply each result by 360°.
Alternatively:
- Divide 360° by the total frequency.
- Multiply each frequency by this number.
If you are given the angles in a pie chart and the total frequency, how do you calculate the individual frequencies?
If you are given the angles in a pie chart and the total frequency, you can calculate the individual frequencies by doing the following:
- Divide each angle by 360°.
- Multiply by the total frequency.
Alternatively:
- Divide the total frequency by 360.
- Multiply each angle by this number.
What sorts of things should you look for when reading and interpreting statistical diagrams?
When reading and interpreting statistical diagrams, you should look for:
- Keys
- Shading
- Axis labels
- The word "frequency"
- Any unusual or unexpected information mentioned
Define anomaly in the context of statistical diagrams.
An anomaly, otherwise known as an extreme value or outlier, is a data point that is significantly different from the rest of the data.
True or false?
You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect.
True.
You may be asked to comment on aspects of a statistical diagram that could be misleading or incorrect, such as uneven gaps in axis values or a missing key.
Define key in the context of statistical diagrams.
In the context of statistical diagrams, a key is a legend that explains the meaning of symbols, colours, or shading used in the diagram.
True or False?
The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages, spread, and unusual data values for the data sets represented by the diagrams.
True.
The purpose of comparing statistical diagrams is to identify and comment on differences or similarities in averages, spread, and unusual data values for the data sets represented by the diagrams.
What should you consider when deciding which measures to compare in statistical diagrams?
When deciding which measures to compare in statistical diagrams, you should consider:
- Whether the mean, median or mode is the appropriate average to use.
- Whether the range or interquartile range is the appropriate measure of spread to use.
- Whether any assumptions or potential issues with the data could affect the reliability of the results and comparisons.
True or false?
You should aim to make at least one pair of comments when comparing statistical diagrams.
False.
You should aim to make at least two pairs of comments when comparing statistical diagrams:
- One pair should compare averages and comment on what this means in the context of the question.
- The other pair should compare spread and comment on what this means in the context of the question.

Sign up to unlock flashcards

By signing up you agree to our Terms and Privacy Policy

Previous:BearingsNext:Histograms

More Revision Notes you might like