Calculating Statistics

Phone.jpgStatistics is concerned with the collection, presentation and analysis of information and data. The Working with Data activity provides practice with some of the statistics mentioned in this topic.

This topic is about the analysis of the information and data.

Mean, Median and Mode

The mean , median and mode of a set of numbers are all types of average.

Mean

The mean of a set of scores is the sum of all of the scores divided by the number of scores.

This is commonly known as the average.
Mode
 The mode is the most frequent score, that is, the one that occurs most often.
Median

The median of a set of values is the middle value when the values have been arranged in order from smallest to largest.

If there are an even number of values, take the mean or average of the middle two values.

 

Example
Answer

For the following set of test results of ten students:

3, 8, 5, 6, 8, 5, 4, 1, 10, 5

Find:

(a) The mean

(b) The mode

(c) The median

(a) The mean

Calculating_Statistics_01.gif
(b) The mode = 5 (occurs 3 times)

(c) Arrange in order:

1, 3, 4, 5, 5, 5, 6, 8, 8, 10

Median is 5

Spread

Often one set of values will be much more spread out than another.

e.g. Two classes sat a test and recorded the following results:

Class A: 4, 4, 5, 5, 6, 6, 6, 7, 7, 8, 8
Class B: 1, ,2, 3, 4, 4, 5, 6, 8, 9, 10

It can be seen that the Class A results are much closer together than the Class B results.

To measure this we can use the range. This is the difference between the highest value and the lowest value.

For Class A the range is 8 − 4 = 4
For Class B the range is 10 − 1 = 9

 

Stem and Leaf Graphs

A stem and leaf diagram or chart provides a means of sorting data into order.

Numbers are split into categories of the first digit(s) and the last digits(s)

e.g. Given the following 20 test scores:

06, 24, 43, 23, 12, 34, 21, 08, 15, 47,
40, 20, 12, 05, 19, 28, 34, 23, 39, 34

Let the stem be the first digit (the tens column). Now enter each of the second digits (the units column) into the leaf part of the diagram.

Calculating_Statistics_02.gif
Calculating_Statistics_03.gif

Using a stem and leaf graph the middle score, the median can be easily found.

There are 20 scores so the median is halfway between the 10th and the 11th scores.

So count in 10 scores from either the top or from the bottom of the stem and leaf graph. As the 10th score is 3 and the 11th score is 3, the median is also 3.

The range can also be found from the stem and leaf graph by taking the lowest value (05) from the highest value (47). The range is 47 − 5 = 42