Measures of central tendency and dispersion

Question 1

Mean

Answer 1

Arithmetic average, add up all the scores and divide by the number of scores

Question 2

What is a strength of using the mean?

Answer 2

Sensitive measure.
Includes all the scores/values in the data set within the calculation.
Represents data set better than median or mode.

Question 3

What is a limitation of using the mean?

Answer 3

May be unrepresentative.
One very large or small number makes it distorted.
The median or the mode tend not to be so easily distorted.

Question 4

Median

Answer 4

Middle value, places scores in ascending order and select middle value. If there are two values in the middle, the mean of these is calculated.

Question 5

What is a strength of using the median?

Answer 5

Less affected by extreme scores.
The median is only focused on the middle value.
In some cases may be more representative of the data set as a whole.

Question 6

What is a limitation of using the median?

Answer 6

Less sensitive than the mean.
The actual values of lower and higher numbers are ignored.
Extreme values may be important.

Question 7

Mode

Answer 7

Most frequent or common value, used with categorical/nominal data.

Question 8

What is a strength of using the mode?

Answer 8

Relevant to categorical data.
When data is discrete i.e. represented in categories.
Sometimes the mode is the only appropriate measure.

Question 9

What is a limitation of using the mode?

Answer 9

An overly simple measure.
The mode may be at one extreme.
It is not a useful way of describing data when there are many modes.

Question 10

What are the three measures of central tendency?

Answer 10

1) Mean
2) Median
3) Mode

Question 11

What are the two measures of dispersion?

Answer 11

1) Range
2) Standard deviation

Question 12

Range

Answer 12

The difference between between highest to lowest value (sometimes 1 is added if values have been rounded up or down).

Question 13

What is a strength of using the range?

Answer 13

Easy to calculate.
Arrange values in order and subtract largest from smallest.
Simple formula, easier than the standard deviation.

Question 14

What is a limitation of using the range?

Answer 14

Does not account for the distribution of the scores.
The range does not indicate whether most numbers are closely grouped around the mean or spread out evenly.
The standard deviation is a much better measure of dispersion in this respect.

Question 15

Standard deviation

Answer 15

Measure of the average spread around the mean. The larger the standard deviation, the more spread out the data is.

Question 16

What is a strength of using standard deviation?

Answer 16

More precise than the range.
Includes all values within the calculation.
Therefore more accurate picture of the overall distribution of data set.

Question 17

What is a limitation of using standard deviation?

Answer 17

It may be misleading.
Can be distorted by extreme values.
Also, extreme values may not be revealed, unlike with the range.