WEEK 4: MEASURES OF CENTRAL TENDENCY

This refers to the center of the distribution of observations

Measures of Central Tendency

What are the 3 common measures of central tendency?

1. Mean

2. Median

3. Mode

Population Mean

Sample Mean

Mean is also known as?

Average

• This is sensitive to extreme observations

• Involves all observations in its computation

• Any change in the observation will change the mean value 

• Quantitative 

• The sum should always be zero because it is the point of balance

Mean

• This is the middle most value in a set of observations put in an array

• Not influenced by outliers

• Always exists and unique

• Can be used for qualitative and quantitative  

Median

Median

TRUE OR FALSE:

If the median is odd, we pick the middle most observation 

TRUE 

TRUE OR FALSE:

If the median is even, get the mean of the 2 middlemost observations 

TRUE 

• Most frequently occurring value in a set of observation

• An observation can have none of this, unimodal, bimodal, or multimodal 

• No calculations are needed

• Determined for any type of variable 

Mode

What are the 3 common measures of dispersion?

1. Range

2. Variance

3. Standard Deviation 

4. Coefficient Variation 

• Gives information as a tendency of values to clump together tools describing the variability of the observations 

• Can be homogeneous or heterogeneous 

• For qualitative variables only 

Measures of Dispersion

• Simplest measure of location

• Does not tell anything about the observation between these two extreme observations 

• May be used for quantitative variables 

Range

Range

Variance

• This is the measure of variability that takes the mean as the reference point

• Involves all observations

• Hard to interpret 

• Unit squared of the original set of observations after subtracting it to the mean 

Variance

• This expresses the SD as percentage of mean

• Most appropriate when the measurement of variables are different and there are 2 or more variables 

Coefficient Variation

Coefficient Variation 

HOMOGENOUS OR HETEROGENOUS:

When the measure of dispersion is low or small 

HOMOGENEOUS 

HOMOGENOUS OR HETEROGENOUS:

When the measure of dispersion is high or large

HETEROGENOUS

• Determines the location/position of particular value in an array of distribution 

• Provide more details about a part of the entire distribution of observations in a give data 

• Use for quali and quanti 

Measures of Location

What are the most common measures of location?

1. Quartiles

2. Deciles

3. Percentiles