Measures of central tendency and dispersion

Question 1

Measures of central tendency

Answer 1

A descriptive statistic that provides information about a “typical” value for a data set.

Question 2

Mean

Answer 2

The arithmetic average of a data set.
Takes the exact values of all the data into account.

Question 3

Mean - process

Answer 3

Calculated by adding up all the data items and dividing them by the number of data items.

Question 4

Mean - evaluation

Answer 4

The most sensitive measure of central tendency.
It takes account of the exact distance between all the values of all the data.
This sensitivity means that it can be easily distorted by one or a few extreme values and therefore end up being misrepresentative of the data as a whole.
It can’t be used with nominal data.

Question 5

Median

Answer 5

The middle value of a data set when the items are placed in rank order.

Question 6

Median - process

Answer 6

The middle value in an ordered list.
All data items must be arranged in order and the central value is then the median.
If there’s an even number of data items there will be two central values.
To calculate the median, add the two data items and divide by two.

Question 7

Median - evaluation

Answer 7

The median isn’t affected by extreme scores.
It can be used with ratio, interval and ordinal data.
On the other hand, the median isn’t as “sensitive” as the mean because the exact values aren’t reflected in the median.

Question 8

Mode

Answer 8

The most frequently occurring value or item in a data set.

Question 9

Mode - process

Answer 9

The value that is most common data item.
With nominal data, it’s the category that has the highest frequency count.
With interval and ordinal data, it’s the data item that occurs most frequently.
To identify this, data items need to be arranged in order.
The modal group is the group with the greatest frequency.
If two categories have the same frequency the data have two modes.
This means the data set is bi-modal.

Question 10

Mode - evaluation

Answer 10

Unaffected by extreme values.
Is much more useful for discrete data.
The only method that can be used when the data are in categories.
For example:
Nominal data.
It’s not a useful way of describing data when there are several modes.

Question 11

Measures of dispersion

Answer 11

A descriptive statistic that provides information about how spread out a set of data is.

Question 12

Range

Answer 12

The difference between the highest and lowest item in a data set.
Usually 1 is added as a correction.

Question 13

Range - process

Answer 13

The arithmetic distance between the top and bottom values in a set of data.
it’s customary to add 1.

Question 14

Range - evaluation

Answer 14

The range is easy to calculate.
However, it’s affected by extreme values.
It also fails to take account of the distribution of the numbers.
For example:
it doesn’t indicate whether most numbers are closely grouped around the mean or spread out evenly.

Question 15

Standard deviation

Answer 15

Shows the amount of variation in a data set.
It assesses the spread of data around the mean.

Question 16

Standard deviation - process

Answer 16

A more precise method of expressing dispersion.
This is a measure of the average distance between each data item above and below the mean, ignoring plus or minus values.
It’s usually worked out using a calculator.

Question 17

Standard deviation - evaluation

Answer 17

A precise measure of dispersion.
All the exact values are taken into account.
It’s not difficult to calculate if you have access to a calculator.
it may hide some of the characteristics of the data set.
For example:
Extreme values.

Question 18

Nominal

Answer 18

Data in separate categories.
For example:
Grouping people according to their favourite football team.

Question 19

Ordinal

Answer 19

Data ordered in sone way.
For example:
Rating how happy you feel that day on a scale of 0-10.

Question 20

Interval

Answer 20

Data measured using units of equal intervals.
For example:
Temperature
(Interval data can drop below the value of 0)

Question 21

Ratio

Answer 21

Example:
Age.
(Ratio data can’t drop below the value of 0)