Statistics Toolkit (Edexcel IGCSE Maths A)

If you know the mean and number of values, you can calculate the total of values by rearranging the mean formula:

If you know the mean and total of the data values, you can calculate the number of values by rearranging the mean formula:

False.

The combined mean of two data sets is not the mean of their two means!

To calculate the combined mean for two data sets

1. Find the overall total of the values from both sets

2. Find the total number of values across both sets

3. Divide the overall total by the overall number of values.

A frequency table is a table that displays data values and their corresponding frequencies.

Frequency is the number of times a particular value occurs in a data set.

To find the mean from a frequency table:

1. Include a column for (value frequency)

2. Sum this column

3. Divide the sum by the total frequency

To find the median from a frequency table:

1. Make sure the values in the table are in order

2. Find the th value, where is the total frequency

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

True.

The mode is the value with the highest frequency.

Discrete data refers to data that can only take certain numerical values, with gaps between the values.

To estimate the mean from grouped data:

1. Find the midpoint of each class

2. Calculate (midpoint × frequency) for each

3. Sum the (midpoint × frequency) values

4. Divide the sum by the total frequency

A class interval is a range of values within which data points are grouped together.

False.

Only an estimate of the mean can be calculated from grouped data.

Continuous data refers to data that can take any numerical value within a range.

To find the class interval containing the median

1. Find the position of the median using , where is the total frequency

2. Use the table to determine the class interval containing this position

To find the modal class interval, look for the class interval with the highest frequency.

The phrase "estimate the mean" usually indicates that the data is grouped, and that you should use the midpoint method to estimate the mean.

The range is the difference between the highest and lowest values in a data set (i.e., highest value minus lowest value).

The interquartile range (IQR) is the difference between the upper and lower quartiles (i.e., upper quartile minus lower quartile).

A quartile is one of the values (lower quartile, median and upper quartile) that divide an ordered data set into four equal parts.

The lower quartile (LQ) is the value below which 25% of the data lies (and above which 75% of the data lies).

The upper quartile (UQ) is the value above which 25% of the data lies (and below which 75% of the data lies).

False.

The range is affected by outliers.

True.

The IQR is not affected by outliers.

Lower quartile th value

• where is the total frequency

Upper quartile th value

• where is the total frequency

The equation for interquartile range (IQR) is  

Where:

• is the upper quartile

• is the lower quartile

Comparing distributions means comparing two or more related data sets, and noting differences or similarities between them.

When comparing distributions, you should compare two things:

• an average for the distributions

• a measure of spread for the distributions

False.

The mean or median are usually used to compare the averages of distributions. The mode can be used for non-numerical data.

The range or interquartile range (IQR) can be used to compare the spread of distributions. The IQR focuses on the middle 50% of the data.

To compare the averages, give the numerical values of the averages, explicitly compare them, and explain what the comparison means in the context of the question.

To compare the spreads, give the numerical values of the range or interquartile range, explicitly compare them, and explain what the comparison means in the context of the question.

When comparing raw data sets, you should check for outliers in either distribution and mention how they may affect the reliability of the results and comparisons.

True.

You should make at least two pairs of comments when comparing distributions, one pair comparing averages and one pair comparing spread.

When comparing distributions, you should also consider any assumptions or potential issues with the data that could affect the validity of the comparisons.

False.

When comparing averages and spread, you must discuss them in the context of the question, not just compare the numbers.

A bar chart is a visual representation of qualitative or discrete data using rectangular bars of equal width.

A pictogram is a visual representation of qualitative or discrete data using repeated symbols or icons.

False.

Bar charts are not used for continuous data.

Bar charts are used for qualitative or discrete data.

To identify the mode from a bar chart, find the bar with the highest height or frequency.

A comparative bar chart is a bar chart that displays two or more data sets side by side for easy comparison.

A key is a legend that explains the meaning of the symbols or colours used in a statistical diagram.

False.

A key is not optional when creating a pictogram.

A pictogram requires a key that specifies the frequency represented by each symbol or icon.

True.

Bar charts should have gaps between the bars.

False.

Pictogram symbols should be of the same size for easy comparison.

(Though a pictogram may use part of a symbol, to represent a frequency that is less than the value of the complete symbol.)

A two-way table is a table that displays data divided according to two characteristics or variables.

Marginal totals, also known as sub-totals or row/column totals, represent the sum of values across rows or columns in a two-way table.

The grand total is the overall sum of all values in a two-way table, found where the row totals and column totals intersect.

To construct a two-way table:

1. Identify the two characteristics

2. Use rows for one characteristic and columns for the other

3. Add an extra row and column for marginal totals

False.

Data items represented in a two-way table must have one (and only one) 'row characteristic' and one (and only one) 'column characteristic'.

When there is overlap between characteristics, a Venn diagram should be used.

False.

When completing a two-way table, some values can be filled in directly, but some values will need to be deduced. For example, subtracting other values in a row from the row total to find a missing value.

You can double-check your answers when completing a two-way table by making sure that all row and column totals add up correctly, and that they match the grand total.

A row total is the sum of values across a single row in a two-way table.

A column total is the sum of values along a single column in a two-way table.

If you get stuck when completing a two-way table, look back at the question for any information you may have missed.

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 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

• multiplying this by 360

Alternatively, you can see how many times 30° goes into 360° and then multiply this by 10.

To calculate the angles needed for a pie chart:

• divide each frequency by the total frequency

• multiply each of these 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, you can calculate the individual frequencies by:

• dividing each angle by 360°

• multiplying by the total frequency

Alternatively:

• divide the total frequency by 360

• multiply each angle by this number

When reading and interpreting statistical diagrams, you should look for keys, shading, axis labels, the word "frequency," and any unusual or unexpected information mentioned.

The purpose of reading and interpreting statistical diagrams is:

• To gather information from the diagram to calculate meaningful statistics like the mean, median, mode, range, and interquartile range

• To make conclusions about the data in the context of the question

An anomaly, or outlier, in the context of statistical diagrams, is a data point that is significantly different from the rest of the data.

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.

False.

When answering an exam question, you should not focus only on the information provided in the statistical diagram or diagrams.

You should also consider any additional information or context provided in the question, not just the information in the diagram itself.

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

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.

When deciding what 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.

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