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In the 11+ Examinations, Mean, Median, Mode and Range is an important topic.The mean, mode, median, and range are averages, which are used in statistics to give information about the data. Mean is the average of all of the numbers. Median is the middle number, when in order. Mode is the most common number. Range is the largest number minus the smallest number.
Let's learn about them one by one.
1. Mean
To find the mean we must add up all the numbers we’re finding the average of, and then divide the total by the number of values.
Mean = Sum of items ÷ Total number of items
To work out the mean:
- Add up all the numbers in the data set.
- Divide the total by the number of values in the set of data.
Let's work out the mean...
Workout the mean of these numbers 12, 6, 2, 6, 11, 3, 10, 14
First add up all the numbers = 12+6+2+6+11+3+10+14=64
Now divide Sum with total numbers which is 8. Mean is 64⁄8=8
1.1. Examples on Finding mean
Example:
9 girls were asked how many pets they had. These are their results,
7,5,1,5,4,3,5,7,8 Find the mean of the result.
Solution: First, add up the numbers.
7+5+1+5+4+3+5+7+8=45
Second, divide the sum with total number of values which is 9
Mean = 45⁄9 (Mean=Sum of items ÷ Total number of items)
Mean of their results = 5
Example:
The pictograph shows how many people were treated for an injury at a clinic in a week.
Calculate the mean number of people treated each day.
Solution: First, write the number of people treated on each day from the graph.
Monday = 4×3=12
Tuesday = 4×5=20
Wednesday = 4×2=8
Thursday = 4×3.5=14
Friday = 4×1.5=6
Second, add up the number of people treated = 12+20+8+14+6=60
Mean= Sum of the people treated each day ÷ Total number of days
Third, divide the sum with the total number of days.
Mean = 60⁄5
Mean= 12
2. Median
Median is a middle term. To find the median, arrange the numbers in ascending order and select the middle term. For example, the median of 1, 2, 3, 4, and 5 is 3.
2.1. Median of Odd and Even number of values.
If n is the number of values in the list, then work out the value n+1⁄2. The median is that number of values in the list. For example, Find the median of 17,8,4,9,13,11,2.
Here the numbers of values n = 7 (odd). so, median = (n+1⁄2)ˆth term.
First arrange the numbers in ascending order 2, 4, 8, 9, 11, 13, 17
Median = (7+1⁄2)ˆth term. Median = 4th term Therefore, median = 9.
Median of Even number of values.
If n is the number of values in the list, then work out the value of n+1⁄2. Median = (n+1)ˆth⁄2 term.
For example, Let's find the median of 17, 8, 4, 6, 13, 11, 2,5. Here the number of values n = 8 (Even) so, Median = (n+1)ˆth⁄2 term. Hence median is 4.5ˆth term. Average of 4ˆth and 5ˆth term
First arrange the numbers in ascending order 2, 4, 5, 6, 8, 11, 13, 17.
Median = (8+1)ˆth⁄2 term. Median = 6+8⁄2=14⁄2=7 Therefore median = 7
2.2. Examples on finding Median
Example: Six pupils went to a Science competition, and their scores are: 20, 15, 14, 20, 15, 13
Solution: First arrange the scores in ascending order.
13, 14, 15, 15, 20, 20
Number of values n = 6 (Even), Hence, Median = (n+1)ˆth⁄2 term. Median=
6+1⁄2= 7⁄2= 3.5ˆth term. Average of 3ˆrd and 4ˆth term
Median = (15+15)⁄2= 30⁄2= 15
Example: Jacqueline noted the number of pages she read in 5 days of the week.
The result is given in the bar chart.
Find the median of the number of pages that she read.
Solution:
First arranging the number of pages read each day in ascending order
Monday = 70
Tuesday= 60
Wednesday = 70
Thursday = 30
Friday = 90
Ascending order = 30, 60, 70, 70, 90
Number of values n = 5(odd)
Median = (n+12)ˆth term
Hence, Median=((5+1)⁄2)=3ˆrd term
Median = 70
3. Mode
The mode is the value that appears the most number of times in a data set. For example, the mode of these values 2, 2, 2, 5, 6, 7 and 8 is 2.
Example: 9 people take a test. Their scores out of 100 are: 56, 79, 77, 48, 90, 68, 79, 92, 71
Solution:
56, 79, 77, 48, 90, 68, 79, 92, 71
The most often score = 79
Hence Mode = 79
Example:
The bar chart below shows the number of pets owned by children in class 5B
What is the modal number of pets?
Solution: 9 children have 2 pets. 8 children have 1 pet and 4 children have 3 pets.
Hence Modal number of pets = 2
4. Range
The range is the difference between the biggest and the smallest number.
To find the range, subtract the lowest number from the biggest number.
For example: 56, 79, 77, 48, 90, 68, 79, 92, 71
48, 56, 68, 71, 77, 79, 79, 90, 92.
Range = Highest values - Lowest value
The range of the above data set is
92-48=44
The range is 44.
Example: The age of five children are 10, 8, 9, 11 and 7 years.
Find the range.
Solution:
Arranging the ages in ascending order
7, 8, 9, 10, 11
Highest value = 11
Lowest value = 7
Range = Highest values - Lowest value
Range =
11-7=4
Example:
The table below shows the maximum temperature in a city in the last six months?
Example:
The table below shows the maximum temperature in a city in the last six months?
| Month | Jan | Feb | March | April | May | June |
| Maximum. temperatures in C° | 2 | 3 | 12 | 20 | 25 | 27 |
Find the range.
Range = Highest values - Lowest value
Range = 27-2=25 C°
