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Chapter Overview
Learning Goals
Learning Goals
Maths
Summary
The mean, median, mode and range are used to compare and analyse data. They tell you information about a set of data such as the average or how big it is.
Sometimes the mean, median, mode and range are referred to as averages but each one has their own definition.
Mean | The average: the total of all the items added up $\div$ the total number of items. |
Median | The middle value. The position can be found by using $\frac{n+1}{2}$ where n is the number of values. (Note: The values MUST be in order from smallest to largest). |
Mode | The most common value. |
Range | The difference between the biggest and smallest |
What is the mean, median, mode and range of the following set of numbers?
$1,4,6,2,3,8,1,2,1,3$
Mean:
$\frac{\text{all the values added up}}{\text{the number of values}} = \frac{1+4+6+2+3+8+1+2+1+3}{10}=\frac{31}{10}=\underline{3.1}$
Median:
First, reorder the values.
$1,1,1,2,2,3,3,4,6,8$
Find the position of the median.
$\frac{n+1}{2} = \frac{11}{2} = 5.5$
Note: Since the position of the median is $5.5$, this means it sits in the middle of the fifth and sixth value. Add them together and divide by two to find the mean.
$(2+3)\div2=\underline{2.5}$
Mode:
The most common number in the sequence.
$\underline1$
Note: Sometimes there could be multiple modes if two values share the same frequency or no mode where all values are repeated the same number of times!
Range:
Take the smallest number away from the biggest number.
$8-1=\underline7$
The mean, median, mode and range are used to compare and analyse data. They tell you information about a set of data such as the average or how big it is.
Sometimes the mean, median, mode and range are referred to as averages but each one has their own definition.
Mean | The average: the total of all the items added up $\div$ the total number of items. |
Median | The middle value. The position can be found by using $\frac{n+1}{2}$ where n is the number of values. (Note: The values MUST be in order from smallest to largest). |
Mode | The most common value. |
Range | The difference between the biggest and smallest |
What is the mean, median, mode and range of the following set of numbers?
$1,4,6,2,3,8,1,2,1,3$
Mean:
$\frac{\text{all the values added up}}{\text{the number of values}} = \frac{1+4+6+2+3+8+1+2+1+3}{10}=\frac{31}{10}=\underline{3.1}$
Median:
First, reorder the values.
$1,1,1,2,2,3,3,4,6,8$
Find the position of the median.
$\frac{n+1}{2} = \frac{11}{2} = 5.5$
Note: Since the position of the median is $5.5$, this means it sits in the middle of the fifth and sixth value. Add them together and divide by two to find the mean.
$(2+3)\div2=\underline{2.5}$
Mode:
The most common number in the sequence.
$\underline1$
Note: Sometimes there could be multiple modes if two values share the same frequency or no mode where all values are repeated the same number of times!
Range:
Take the smallest number away from the biggest number.
$8-1=\underline7$
Mean, median, mode and range
FAQs
Question: What is the range?
Answer: The range is the difference between the biggest and smallest values.
Question: What is the mode?
Answer: The mode is the most common value.
Question: What is the median?
Answer: The median is the middle value. It's position can be found by using (n+1) divided by two. (Note: the values MUST be in order from smallest to largest).
Question: What is the mean?
Answer: The mean is the average: the total of all the items added up divided by the total number of items.
Theory
Exercises
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