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