The mean and standard are the most widely used statistical tools in educational and psychological research.The mean is the most frequently used measure of central tendency while the standard deviation is the most frequently used measure of variability or dispersion.
Σ
Computing the Mean
The mean or X (pronounced as X bar) is the figure obtained when the sum of all the items in the group is divided by the number of items (N). Say for example you have the score of 10 students on a science test.
The sum ( ) of all the ten scores = 23 + 22 + 26 + 21 + 30 + 24 + 20 + 27 + 25 + 32 = 250
Σ (X ) 250
= = 25.0
N 10
Mean or X =
In the computation of the mean, every item counts. As a result, extreme values at either end of the group or series of scores severely affects the value of the mean. The mean could be "pulled towards" as a result of the extreme scores which may give a distorted picture of the groups or series of scores or data.
However, in general, the mean is a good measure of central tendency for roughly symmetric distributions but can be misleading in skewed distributions (see example below) since it can be greatly influenced by extreme scores.
Mean Influenced by Extreme Score
If we were to change the first score from 23 to 75, see what happens to the mean
The extreme score has changed the mean to 30.2 which may give the impression that students performed better in the test when in fact only one student scored high.
NOTE:Keep in mind this characteristic when interpreting the means obtained from a set of data.
INTRODUCTION - 3
SELF-CHECK
a) What is a sample?
b) Why is a sample used in educational research?
c) What is statistical induction?
Variables
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STANDARD DEVIATION
When you give a test, there is bound to be variation in the scoers obtained by students. Variability or variation or dispersion is determined by the distance of a particular score from the 'norm' or measure of central tendency such as the mean. The standard deviation is a statistic that shows the extent of variability or variation for a given series of scores from the mean.
The standard deviation makes use of the deviations of the individual scores from the mean. Then each individual deviation is squared to avoid the problem of plus and minus. The standard deviation is the most often used measure of variability or variation in educational and psychological research.
The following is the formula for calculating the standard deviation:
In the computation of the mean, every item counts. As a result, extreme values at either end of the group or series of scores severely affects the value of the mean. The mean could be "pulled towards" as a result of the extreme scores which may give a distorted picture of the groups or series of scores or data. 
