ENGDAN 03: Measures of Central Tendency, Measures of Dispersion

measure of central tendency

is a descriptive statistic that describes the average or typical value of a set of scores

mode

the score that occurs most frequently in a set of data

median

• another name for the 50th percentile

• the score in the middle — half the scores are larger, and half the scores are smaller than the median

mean

arithmetic average of all the scores

1. readily comprehensible and easily calculated

2. best representative of data

3. not affected by the extreme value

4. can be determined graphically

5. actual value of an important part of the series

advantages of mode

1. not based on all observations

2. not capable of further mathematical manipulation

3. affected to a great extent by sampling fluctuation

4. influenced by choice of grouping

disadvantages of mode

1. can be calculated in all distributions

2. can be understood by common people

3. can be ascertained even with extreme values

4. can be located graphically

5. most useful when dealing with qualitative data

advantages of median

1. not based on all values

2. not capable of further mathematical treatment

3. affected by fluctuation of sampling

4. in case of even number of values, it may not be the value from the data

disadvantages of median

1. it is easy to understand and calculate

2. based on all values

3. it is rigidly defined

4. easy to understand even when data is lacking

5. isn’t based on the position of the series

advantages of mean

1. it is affected by the extreme value

2. can’t be calculated for open-ended classes

3. cannot be located graphically

4. gives misleading conclusions

5. has upward bias

disadvantages of mean

dispersion

• the scatteredness of the data series around its average

• the extent to which values in a distribution differ from the average of the distribution

1. it should be rigidly defined

2. should be easy to understand and calculate

3. should be based on all observations of the data

4. should be subjected to further mathematical treatment

5. should be least affected by sampling fluctuation

6. should not be unduly affected by the extreme values

characteristics of an ideal measure of dispersion

range

• the simplest measure of dispersion

• the difference between the extreme values of a series

1. simplest and most crude measure of dispersion

2. not based on all observation

3. unduly affected by extreme values and sampling fluctuations

4. may increase with the size of set observations

5. gives an idea of the variability very quickly

characteristics of range

1. ignores the way in which data is distributed

2. sensitive to outliers

disadvantages of range

quartile measures

splits the ranked data into four segments with an equal number of values per segment