Descriptive Statistics

Measures of central tendency

Explain what the mean is

Mean: is the average which is

calculated by adding all the

values together and dividing

the total by the number of

scores.

Used with interval data (exact

scores).

What are the strengths of the mean?

Is the most sensitive

measure of central

tendency because

individual values are used.

• It is the most representative

measure of central

tendency because the

whole data set is used. This

is why it is commonly used

with interval data

What is the limitation of the mean?

Can be misrepresentative if

there are extreme high or

low scores (outliers) in a

data set. If this is the case,

the median should be used.

Explain what the median is

: is the central value

in a list of ranked values. With

an even number of values,

the median is the mid-point

between the two values.

Used with ordinal data

(ratings/ranked data).

What is the strength of the median?

It is not affected by outliers

because it focuses only on

scores in the middle of the

distribution. Therefore, it is

better with skewed data

than the mean

What is the limitations of the median?

Not as sensitive as the

mean; although the whole

data set is used when

ordering, not all individual

values are used.

• It is time consuming in a

large data set to organise a

group of numbers in

ascending order.

Explain what the mode is

: is the most common

value in a set of scores. There

may be two modes (bi-modal)

or no mode if all the scores

are different.

Used with nominal data

(categorical data).

What is a strength of the mode?

It is useful when the data is

in categories as it can be a

more appropriate way of

describing the data

compared to the mean.

What are the limitations of the mode?

Not as sensitive as other

measures; although the

whole data set is used, no

numerical values are used.

• Not useful with several

modes in a data set.

• May not be representative

of the data set if the most

frequent item is extremely

high or low.

Measures of Dispersion

Explain what the range is

is calculated by

subtracting the lowest value

from the highest value in a data

set.

A larger range indicates that the

values in a data set are more

variable (less consistent) due to

individual differences.

What is the strength of the range?

• Quick and easy to calculate

because it only uses the

highest and the lowest score

in the data set compared to

the standard deviation

which is more complex to

calculate.

What are the limitations of the range?

Distorted by outliers

because it only uses the

lowest and the highest

score in the data set.

• Does not show whether

data are evenly spread

above and below the

mean

Explain what standard deviation is

is

calculated by working out the

average distance of each value

from the mean.

A larger SD indicates that the

values in a data set are more

variable (less consistent) due to

individual differences.

What are the strengths of the standard deviation?

• More sensitive and precise

than the range since all

values are used in the

calculation.

• It allows for the

interpretation of individual

scores in relation to the SD,

when scores are normally

distributed.

What are the limitations of the standard deviation?

• More complicated and

time consuming to

calculate compared to

the range.

• As it uses the mean, it is

distorted by extreme

scores which make it less

representative of the

data set

Explain how to calculate Standard Deviation

1. Calculate the mean (x)̄: Add up all the values and divide by the number of values.

2. Subtract the mean from each individual value (x-x)̄.

3. Square each value (x-x̄

2

) (removes any minus signs).

4. Add up the squared values (Σx-x̄

2

).

5. Calculate the variance: Divide sum of squared values by number of scores minus 1 (N-1).

6. Calculate the square root of the variance. (reverses the squaring operation in step 3