Averages, Ranges & Data (Edexcel GCSE Maths)

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.

To estimate the mean from grouped data:

1. Find the midpoint of each class.

2. Calculate (midpoint × frequency) for each class.

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.

To find the class interval containing the median from grouped data:

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 from grouped data, 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).

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

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

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 the interquartile range (IQR) is  

Where:

• is the upper quartile

• is the lower quartile

When comparing distributions, you should compare two things:

• An average for the distributions, e.g. mean, median or mode.

• A measure of spread for the distributions, e.g. range or IQR.

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:

1. Give the numerical values of the averages,
   e.g. data set A has a mean of 43.5 and data set B has a mean of 53.7.

2. Explicitly compare them,
   e.g. the mean of set B is greater than the mean of set A.

3. Explain what the comparison means in the context of the question,
   e.g. this means that, on average, the people in set B take longer on the task than the people in set A.

To compare the spreads:

1. Give the numerical values of the range or interquartile range,
   e.g. set A has a range of 7, set B has a range of 10

2. Explicitly compare them,
   e.g. the range of set B is greater than the range of set A.

3. Explain what the comparison means in the context of the question,
   e.g. this means that the times taken by individuals in set B is more spread out than the times taken by individuals in set A.

True.

When comparing raw data sets, you should check for extreme values 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.

True.

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

E.g. when assessing the water quality of a river, the samples may have all been taken from one place so may not be representative of the whole river.

False.

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

Qualitative data is data that is usually given in words, not numbers, to describe something.

For example, the colour of a teacher's car.

False.

The number of pets that a student has is an example of quantitative data as it is numerical.

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

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

False.

Age can be discrete or continuous depending on the context or how it is defined.

If you mean how many years old a person is, then it is discrete.

If you mean how long a person has been alive, then it is continuous.

True.

Primary data is data that has been collected by the person carrying out the research, such as through questionnaires, surveys, or experiments.

Secondary data is data that has been collected previously, found on the internet or through other research sources.

For example, the number of wins for each football team in a previous World Cup.

False.

A population does not necessarily refer to a number of people or animals.

It can refer to any set of items being studied, such as all the different makes and models of mobile phones in the world.

A sample is a selected part (called a subset) of the population which is used to collect data from.

One advantage of using a sample for data collection is that it is quicker to collect the data compared to using the entire population.

Alternative reasons are that it is cheaper or it is easier to analyse as there is less data.

The equation for the capture-recapture method is

Where:

• is the number in the second sample that have marks/tags

• is the total number in the second sample

• is the total number in the first sample (all of which are marked/tagged)

• is the size of the population

This can be rearranged to to estimate the size of a population.

True.

In the capture-recapture method, all captured animals in the first sample are released back into the population after being tagged.

It is assumed that the population remains the same size (broadly speaking) between the first and second samples.

Time is needed for the tagged members to have sufficient opportunity to mix with the rest of the population.

True.

In the capture-recapture method, it is assumed that each member of the population has an equal chance of being selected in both the first and second samples.