1. Descriptive statistics
Measures of central tendency
Measures of spread

2. Mean – ungrouped data Mean= Sum of values of items Number of items
Examples of use:
Household consumption
Energy consumption
Car mileage

3. Example 1: What is the Mean of these numbers?
6, 11, 7
Add the numbers:  = 24
Divide by how many numbers
(there are 3 numbers): 24 / 3 = 8
The Mean is 8

4. Example 2: The following is the amount of marks students gained in a recent test. 3, 7, 5, 13, 20, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29 Calculate the mean value?

5. Median ‘Md’
Divides the population into two equal parts, useful when the distribution is skewed, as is resistant to extreme values.
What is the median value? Median is the middle figure. i)

6. ii) Example: 
3, 13, 7, 5, 21, 23, 39, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
There are fifteen numbers. Our middle is the eighth number:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 39, 40, 56
The median value of this set of numbers is 23.

7. Example:
3, 13, 7, 5, 21, 23, 23, 40, 23, 14, 12, 56, 23, 29
When we put those numbers in order we have:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
There are now fourteen numbers and so we don't have just one middle number, we have a pair of middle numbers:
3, 5, 7, 12, 13, 14, 21, 23, 23, 23, 23, 29, 40, 56
In this example the middle numbers are 21 and 23.
To find the value halfway between them, add them together and divide by 2:
= 44 then 44 ÷ 2 = 22
So the Median in this example is 22.

8. Wages /remuneration
Body Mass Index
Hospital stay

9. What is the mode?
mode
Wsq 8-10

10. Mode is the most popular value
For example, students results were as follows
15,20,20,12,15,30,18,19,21,15.
15 appears more often than any other value and therefore is the Mode.
You can have two modes
For example in the following data 20,22,21,22,20,23,19. The mode is both 22 and 20. This is called bimodal.

11. 5 Measures of spread / Dispersion
(a) Range
(b) Interquartile range and quartile deviation
(c) Mean absolute deviation
(d) Standard deviation
(e) Coefficient of variation

12. Highest minus the lowest value
What is the Range?
Highest minus the lowest value
6, 10, 14, 19, 26, 34, 42, 50
50 – 6 = 44
Easy to understand
Affected by extremes
No indication of spread between the extremes
Not suitable for further statistical analysis

13. The variance ‘σ²’ and the standard deviation

14. The population variance, σ²
The variance is the average of the squared mean deviation for each value in a distribution , σ is the greek letter sigma. The variance is therefore called ‘sigma squared’
To arrive at the standard deviation we must find the square root of the variance.

15. Both sets have the same mean,
Why bother?
Consider the two data sets below : -
1, 7, 12, 15, 20, 22, 28
1, 15, 15, 15, 15, 16, 28
What do you notice about the mean, median and range?
Both sets have the same mean,
median and range

16. What is standard deviation ?
The Standard Deviation is a measure of how spread out numbers are.
Its symbol is σ (the greek letter sigma)
The formula is easy: it is the square root of the Variance. So now you ask, "What is the Variance?"
The best measure of spread.
Not ideal if the data is skewed
Note: Variance ‘σ ‘ = standard deviation2
Standard deviation = √σ

17. Consider 0, 1, 0, 3, 5 Five boxes of finished components are chosen at
random and checked for quality control. The
following numbers of faulty components were found
in each box:
0, 1, 0, 3, 5
Question: Calculate the standard deviation

18. Step one Calculate the Mean.
calculate the mean or ‘x’
Mean, x = ( )/5
= 9/5
= 1.8

19. (a bigger σ = bigger spread
Step 2
Calculate the variance σ
Variance is the average of the squared differences from the Mean.
(0 -1.8)2 + (1 -1.8)2 + (0 -1.8)2 + (3 -1.8)2 + (5 -1.8)2 5
σ= 18.8 ÷ 5
σ = 3.76
or n- 1 for a sample
(a bigger σ = bigger spread

20. Step 3 Calculate the standard deviation Standard deviation= √3.76
= 1.94 spread

21. Using the Computer, test your knowledge of Mean, Mode and Median.
There are questions near the bottom to test your knowledge.
mean.html&qs=691_1453_1454_692_1455_1456_2179_2180_3053_ 3054