1.4 Measures of Central Tendency

Mean – the sum of all entries divided by the number of entries

Median – if there is an odd number of entries, the middle entry.

if there is an even number of entries, the average of the two middle ones.

Mode - the entry that appears the most often. It is possible for a data set to be bimodal, if it has two modes.

Ex 1 Find the mean, median, and mode for the following data sets:

(a) 13, 12, 15, 13, 18, 14, 16, 15, 15, 17

(b) Grouped Data

Data Value (x)	Frequency (f)
3 4 5 6 7 8 9	1 1 3 7 15 8 5
Total	40	278

(c) Grouped Continuous Data

When data has been grouped we use the midpoint to represent all the scores in the interval. The midpoint of an interval is the average of the endpoints.

Interval	Frequency	Midpoint
0 – 50 – 100 – 150 – 200 – 250 –	12 20 24 23 17 6
Total	102		14300

Calculating the mean or median of grouped continuous data is always approximate. Discussing the mode of grouped continuous data is always done by class.

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