D3 - Representing Data Numerically

Question 1

Mean

Answer 1

Advantages
>Most used average
>Uses all data

Disadvantages
>Includes anomalies

Example
1, 50, 52, 56, 56, 56, 58
Mean = (1+50+52+56+56+56+58)/7=47

Question 2

Median

Answer 2

Advantages
>Only looks at the middle value so isn’t affected by anomalies

Disadvantages
>Can be misleading as doesn’t consider all data

Example
1, 1, 1, 4, 56, 56, 58
Median is the 4th value –> 4

Question 3

Mode

Answer 3

Advantages
>Easy to find
>No calculation needed
>Only method that can be used with qualitative data

Disadvantages
>Can be misleading - inappropriate if the data contains a few repeats

Example
1, 1, 1, 4, 56, 56, 58
Mode is 1

Question 4

Quartiles

Answer 4

Advantages
>They divide the data into four equal groups

Disadvantages
>Not easy to calculate if the data set is small

Example
Lower Quartile, Median, Upper Quartile 
0, 3, 7, 10, 12, 17
Median - between 7 and 10 - 8.5
LQ - (0, 3, 7) - 3
UQ - (10, 12, 17) - 12

Question 5

Range

Answer 5

Advantages
>It measures the spread of the data

Disadvantages
>It only uses the two extreme values, which may not be representative of how the data is spread

Example
1, 51, 51, 54, 56, 56, 98
Range is 98-1=97 but without the end values it would be 5.

Question 6

Interquartile Range (IQR)

Answer 6

Advantages
>Measure the range of the middle 50% of the data so it’s not influences by extreme values

Disadvantages
>Half the data plays no part in the measure of spread

Question 7

Percentile

Answer 7

A value below which a given percentage of the observations fall

Question 8

Standard Deviation

Answer 8

A measure of spread that uses all data.

Spread around the mean