Measures of central tendency

Measures of central tendency are averages which use a single number to describe what is typical within a data set. The mode is the most commonly occurring value or response. This measure of central tendency is used when you have nominal data (see below). For example, 

Goldfield and Steven Reznick (1990) divided the 18 children in their study into two groups; those who experienced a vocabulary explosion (n=13) and those who did not (n=5). The modal category (mode) was therefore explosion, as it was the most commonly occurring category. Of the ‘exploders’, two exploded between 14 and 16 months, five exploded between 17 and 19 months and six exploded between 20 and 22 months so exploding between 20-22 months is modal as this was the age when most children (n=6) experienced their explosion. 

If you have data that is at least ordinal, you can use the median. This measure of central tendency should also be used if your data set contains outliers as it will provide a better presentation of the data than the mean. Put all the data points in ascending order and choose the middle value. If there are an even number of data points you need to add together the two middle values and divide by two.If your data is interval, you can use the mean. Goldfield and Steven Reznick (1990) quoted the mean number of words acquired during the vocabulary explosion for each of the three groups. The early exploders (n=2) had a mean of 134 words. This was calculated by adding the total number of words that each infant had acquired (167 +101) and dividing by two (268/2=134). The later exploder group had a mean of 101.2 with scores from 75 to 120.