Functional Skills: Mean, Median, Mode and Range

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Functional Skills: Mean, Median, Mode and Range Revision

Mean, Median, Mode and Range

The mean, median and the mode are different measures of the average value of a data set. The range is a measure of spread.

There are 5 skills you need to learn.

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Skill 1: Finding the Mean

Whenever people talk about an average value, they are usually referring to the mean. To calculate the mean, we need to add up all the values and divide by the number of values:

\text{Mean} = \dfrac{\text{Total of values}}{\text{Number of values}}

Note: the mean is affected by outliers – values that lie far outside the rest of the data.

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Skill 2: Finding the Median

The median is the ‘middle value’ of a data set. In order to find the median, we first have to put the data in order of size. There are then two methods we can use:

  1. Cross out the first and last values, then the second and second last values and so on. Eventually we will be left with one or two numbers, depending on whether we had an odd or even number of values to begin with. If only one value is left, this is the median; if two values are left, the median is halfway between the two.
  2. Let the number of values we have to begin with be n. We can calculate the position of the median value using the formula:

\text{Median} = \dfrac{n+1}{2}

Whatever number the formula gives, we count that number along the list of values. If the formula gives us a decimal, e.g. 10.5, the median is half-way between the tenth and eleventh values.

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Skill 3: Finding the Mode

The mode is the most frequent value in a data set. Finding the most is simple – just look for the value that occurs the most often.

Note: it is possible to have more than one mode or no mode at all if there are no repeated values.

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Skill 4: Finding the Range

Unlike the mean, median and mode, the range is not a type of average. The range is a measure of spread – it tells us how spread out our data is. To find the range, we subtract the smallest value from the largest value:

\text{Range} = \text{Largest value}-\text{smallest value}

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Skill 5: Using Averages to make Predictions

You can use averages to make estimates and predictions. You have to make assumptions when making predictions.

Example: Jordan spends £120 on food in January, £220 on food in August and £200 on food in November.

Calculate the mean to estimate how much Jordan spends on food in one year.

 

Calculate the mean by adding up the values and dividing by 3:

mean = \dfrac{£120+£220+£200}{3} = \dfrac{£540}{3} = \textcolor{red}{£180}

Now, assume that Jordan spends \textcolor{red}{£180} each month.

Then, an estimate for the total amount of money Jordan spends on food in one year is:

\textcolor{red}{£180} \times 12 = \textcolor{blue}{£2160}

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Example 1: Finding the Mean and Range

Ryan measures his height and the height of six of his friends. Their heights in cm are:

155, 160, 153, 173, 164, 162, 160

Find the mean and range in their heights.

[2 marks]

First to find the mean, we need to add up the values and divide by the number of values, which is 7:

155+160+153+173+164+162+160=1127

\text{Mean}=\dfrac{1127}{7}=161 cm

 

The range is the difference between the largest and smallest value:

\text{Range} = 173-153=20 cm

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Example 2: Finding the Median and Mode

Ryan measures his height and the height of six of his friends. Their heights in cm are:

155, 160, 153, 173, 164, 162, 160

Find the median and mode in their heights.

[2 marks]

First to find the median, we need to put the heights in order:

153, 155, 160, 160, 162, 164, 173

We will cross out the first and last values, then the second and second last values, and so on, working inwards:

\cancel{153}, \cancel{155}, \cancel{160}, 160, \cancel{162}, \cancel{164}, \cancel{173}

So the median is 160 cm.

 

The mode is the most frequent value. There is only one value that appears twice, so the mode is 160 cm

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Functional Skills: Mean, Median, Mode and Range Example Questions

To calculate the mean, add up all the numbers and divide by the number of values:

 

\text{mean} = \dfrac{5+8+7+4+8+3+1+12}{8}=6

First, we need to put the numbers in order:

 

85, 91, 98, 110, 114, 123

 

Crossing out the numbers on the end and working inwards leaves us with:

 

\cancel{85}, \cancel{91}, 98, 110, \cancel{114}, \cancel{123}

 

The median is halfway between 98 and 110.

 

We can calculate the median by:

 

\text{median}=\dfrac{98+110}{2}=104

The mode is the most common value, which in this case is 8

The range is the difference between the largest and smallest values.

 

\text{range}=256-104=152

To calculate the median, first put the numbers in order:

 

0, \, 1, \, 3, \, 4

 

There are two middle values, so the median is half way between these values:

 

median = 2

 

Now, assume that Mr Ding has 2 sick days each month.

Therefore, an estimate for the number of sick days Mr Ding has is:

 

2 \times 12 = 24 sick days

Additional Resources

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Exam Tips Cheat Sheet

FS Level 2
PFS

Formula Booklet

FS Level 2

Functional Skills: Mean, Median, Mode and Range Worksheet and Example Questions

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Mean and Range L1

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Mean, Median, Mode and Range L2

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