Mean/Median/Mode/SD

Strength of the mean

+’Sensitive’ measure as it reflects the values of all the data in the final calculation

Weakness of mean

Can be unrepresentative of the data set if there are extreme values

Set A: 5, 7, 8, 11, 12, 16, 18

mean = 11.0

Set B: 5, 7, 10, 11, 14, 17, 41

mean = 15.0

(Note: In both data sets the median and mode are the same.)

Strength of median

+Unaffected by extreme scores

Weakness of median

Not as ‘sensitive’ as the mean because not all values are reflected in final calculation

Strength of mode

Useful when data is in categories (nominal data)

Weakness of mode

Not useful way of describing data when there are several modes

Strength of range

+easy to calculate

+convenient way to express how spread out data set is

Weakness of range

-Affected by extreme values

-Fails to take account of the distribution of the data set as it doesn’t indicate whether most numbers are closely grouped around the mean or spread out evenly

Strength of SD

+Precise measure of dispersion because all exact values are taken into account

+easy to calculate with calculator

Weakness of SD

-Can’t be immediately sensed from the data, whereas range is fairly quick to identify

-May hide some of the characteristics of the data set (eg:extreme values)

What is normal distribution?

Mean = median = mode

How much of the data lies within ___ of the mean?

1SD

2SD

3SD

1SD = 68%

2SD = 95%

3SD = 99%

Draw a positive skew

Draw a negative skew

In a positive skew, is the mode, median or mean the highest?

Mode < median < mean

In a negative skew, is the mode, median or mean the highest?

Mean < median < mode