Question

Psychology, statistics

1) Give three specific examples of when a mode would be the optimal measure of central tendency.

2) For each of your three QUALITATIVE variables in #1 create a QUANTITATIVE variable by providing an operational definition which contains a general description and a rating scale. Define each one of the items in your rating scale by OBSERVABLE behaviors.

3) For each of your operational definitions in # 2 determine whether the mean or the median would be the optimal measure of central tendency and for each, explain why.

Answer 1

1) The mode is the least used of the measures of central tendency and can only be used when dealing with nominal data. For this reason, the mode will be the best measure of central tendency (as it is the only one appropriate to use) when dealing with nominal data. The mean and/or median are usually preferred when dealing with all other types of data, but this does not mean it is never used with these data types.

Nominal scales are used for labeling variables, without any quantitative value. “Nominal” scales could simply be called “labels.”

Let us use the example of 3 situations where we can use Mode.

i) What is your gender?

a) M- Male

b) F- Female

c) NA

ii) What is your hair color?

a) Brown

b) Black

c) Blonde

d) Other

iii) Where do you live?

a) USA

b) Not in USA

2) Now for each situation let us assume that we have 5 observations:

i) What is your gender?

a) M- Male

b) F- Female

c) NA

Observations: a, a, b, b, b

We have 2 Male and 3 Female

ii) What is your hair color?

a) Brown

b) Black

c) Blonde

d) Other

Observations: a, a, b, b, c

We have 2 black, 2 brown and 1 observation with Blonde hair.

iii) Where do you live?

a) USA

b) Not in USA

Observations: a, a, a, a, a

We have all 5 as USA.

3) The mean is usually the best measure of central tendency to use when your data distribution is continuous and symmetrical, such as when your data is normally distributed. However we see in the above example that our data is not uniformly distributed. Hence mean wouldn't be appropraite.

The median is usually preferred to other measures of central tendency when your data set is skewed (i.e., forms a skewed distribution). Since if we see that for the third example all the values are USA hence our data is higly skewed. Here median would be a suitable choice.