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