Analysing Our Results From Our Tests
Looking at our data!
What is Mean, Median, Mode and Range? Give examples
Which is the best average Mean, Median and Mode? Why?
The mean
The mean is the most commonly used average.
To calculate the mean of a set of values we add together the values and divide by the total number of values.
Mean =Number of values
Sum of values
For example, the mean of 3, 6, 7, 9 and 9 is
3 + 6 + 7 + 9 + 9
5=
5
34= 6.8
Finding the mode
The mode or modal value in a set of data is the data value that appears the most often.For example, the number of goals scored by the local football team in the last ten games is:
The modal score is 2.
Is it possible to have more than one modal value?
Is it possible to have no modal value?
Yes.
Yes.
2, 1, 2, 0, 0, 2, 3, 1, 2, 1.2, 1, 2, 0, 0, 2, 3, 1, 2, 1.
Finding the median
The median is the middle value of a set of numbers arranged in order. For example:
Find the median of
10, 7, 9, 12, 7, 8, 6,
Write the values in order:
6, 7, 7, 8, 9, 10, 12.
The median is the middle value.
Finding the median
When there is an even number of values, there will be two values in the middle.In this case, we have to find the mean of the two middle values.
Find the median of 56, 42, 47, 51, 65 and 43.
The values in order are:
There are two middle values, 47 and 51.
42, 43, 47, 51, 56, 65.
Rogue values
The median is often used when there is a rogue value – that is, a value that is much smaller or larger than the rest.
The mean of the data set is 168. This is not representative of the set because it is lower than almost all the data values.
What is the rogue value in the following data set:192, 183, 201, 177, 193, 197, 4, 186, 179?
The median of this data set is:
4, 177, 179, 183, 186, 192, 193, 197, 201.
The median of the data set is not affected by the rogue value, 4.
If the range is large, it tells us that the values vary widely in size.
If the range is small, it tells us that the values are similar in size.
Finding the range
The range of a set of data is a measure of how the data is spread across the distribution.To find the range we subtract the lowest value in the set from the highest value.
Range = highest value – lowest value
Mean or median?
Would it be better to use the median or the mean to represent the following data sets?
median
mean
mean
median
mean
median
34.2, 36.8, 29.7, 356, 42.5, 37.1?
0.4, 0.5, 0.3, 0.8, 0.7, 1.0?
892, 954, 1026, 908, 871, 930?
3.12, 3.15, 3.23, 9.34, 3.16, 3.20?
97.85, 95.43, 102.45, 98.02, 97.92, 99.38?
87634, 9321, 78265, 83493, 91574, 90046?
Mean, Median or Mode?
Transport Car Train Bus Tram
Number of people
8 5 13 5
Mean, Median or Mode? Problem 2
Calculating the mean using a spreadsheet
When processing large amounts of data it is often helpful to use a spreadsheet to help us calculate the mean.
For example, 500 households were asked how many children under the age of 16 lived in the home. The results were collected in a spreadsheet.
How do we Measure Health and Fitness?
The tests
Sit & Reach test
Beep test
Standing Broad Jump test
Ruler Drop test
Vertical Jump test
What kind of information would you like to find out about the class?
• Some suggestions• Are girls fitter than boys?• Is 7R fitter than 7N?
Are 10 year olds fitter than 11 year olds? Go back to your classrooms to discuss what you would like to find out about.
• Present
Questions?
• DOES height affect flexibility?• Are tall people fitter than short people?• Is 7R fitter than 7N?• Do boys have more stamina girls?• Is 7R sporty than 7N? • Is 7R fitter than the rest of year 7
Top Related