Mate

Chapter 3 Statistical Summary
This topic covers:  The concept and measures of central tendency for ungrouped and grouped data.  The concept and measures of dispersion for ungrouped and grouped data.

Introduction
 When we look at a distribution of data, we should consider three characteristics: Shape (chapters 2 and 4) Center / Location (central tendency measurement) Spread (dispersion measurement)  With these characteristics, we can numerically describe the main features of a data set.  And, we may describe about the behaviour of the data in much simpler form.

Centre/location

Shape

Spread

Central Tendency Measurement
 A measure of central tendency gives the center of a histogram or a frequency distribution. To report a typical value that is representative of the data.  Three common measures of central tendency:
 Mean (Arithmetic mean)  Median  Mode

 Other measures of central tendency:
 Trimmed mean  Harmonic mean  Geometric mean

CENTRAL OF TENDENCY

Scale type

Permissible central of tendency

Nominal

Mode

Ordinal

Median

Interval

Mean, Mode*, Median* All statistics are permitted including geometric mean, harmonic mean, trimmed mean, and other robust means.

Ratio

Central tendency for Ungrouped Data

Mean (Arithmetic mean)
 The most frequently used measure of central tendency.  The mean of a data set is the sum of the observation divided by the number of observation.

Population Data

Sample Data

Median
 The median is the value of the middle term in a data set that has been ranked in increasing order.  Steps: 1) Rank the data in increasing order. 2) Determine the depth (position) of the median.

3) Determine the value of the median.

Mode
 The mode of the data set is its most frequently occurring values.  Not unique. No mode – a data set with each value occurring only once (e.g. 3,4,5,6,1,2,7,8). Unimodal – a data set with only one value occurring with the highest