Measures of Central Tendency

central tendency

• This is a method of calculating the average of a set of data

• The average represents the centre  of the distribution

• These types of statistics are descriptive which means they seek to summarize the data

mean, median, mode

The three common methods of finding the average are:

mean

• arithmetic average of a group of scores; sum of the scores divided by the number of scores

• the balance point of a distribution 

modified histogram

the balance point of a distribution

weighted mean

• an average in which each observation in the data set is assigned or multiplied by a weight before summing to a single average value.

weighted mean formula

is used to calculate an average where each value has a different level of importance  (weight)

characteristics of the mean

1. Changing a score in the distribution can affect the value of the mean 

2. Introducing a new score or removing a score can affect the value of the mean

3. Adding or subtracting a constant from each score will change the value of the mean

4. Multiplying or dividing each score by a constant will change the value of the mean

when to use the mean

• very commonly used in quantitative research, especially in psychological studies

• approximately normally distributed data

• with equal-interval variables

                            -continues data/variable

                            -interval/ratio

median

• middle score when all the scores in a distribution are arranged from lowest to highest.

steps for finding the median

1. Line up all scores from lowest to highest.

2. Figure how many scores there are to the middle scores by adding 1 to the number of scores and dividing by 2.

3. Count up to the middle score or scores.

when to use the median

1. with rank-ordered variables

2. non-normal or skewed distributions

3. when a distribution has one or more outliers

4. rarely used in psychology research

outliers

a score with an extreme (very high or very low) in relation to other scores in the distribution 

mode

• value with the greatest frequency in the distribution.

when to use the mode

• with categorical variables (nominal)

• rarely used in psychology research

unimodal distribution

• frequency distribution with one value clearly having a larger frequency than any other.

bimodal distribution

• frequency distribution with two approximately equal frequencies, each clearly larger than any others.

multimodal distribution

• frequency distribution with two or more high frequencies seperated by a lower frequency.

rectangular distribution

• frequency distribution in which all values have approximately the same frequency.

symmetrical distribution

• distribution in which the pattern of frequencies on the left and right side are mirror images of each other.

skewed distribution

• distribution in which the scores pile up on one side of the middle and are spread out on the other side; distributions that are not symmetrical

positively skewed distribution

• the peak (highest frequency) in the distribution is on the left-handside with tail tapering off the right

floor effect

• situation in which many scores pile up at the low end of a distribution (creating a skewness to the right) because it is not possible to have any lower score.

negatively skewed distribution

• the peak (highest frequency) in the distribution is on the right-hand side with the tail tapering of the left

ceiling effect

• situation in which many scores pile up at the high enf of a distribution (creating a skewness to the left) because it is not possible to have a higher score.

kurtosis

• extent to which a frequency distrbution deviates from a normal curve in terms of whether its curve in the middle is more peaked or flat than the normal curve.

leptokurtic

• the scores are concentrated towards the mean.

mesokurtic

• normal curve

platykurtic

• the scores have an extremely large deviation (departure o pag-layo) from the mean.

normal distribution

• bell-shaped frequency distribution that is symmetrical and unimodal.

• distributions observed in nature and in research commonly approximates it.