2. Marks awarded by counting the number of
correct answers on a test script are known
as raw marks.
Chandralatha got 16 marks out of 20 for
Psychology at the monthly test.
Is it a high mark or a low mark? What do
you think?
3. It may appear a high mark, but in fact the
statement is virtually meaningless on its
own.
16 may be the lowest mark of a particular
group of scores. If the test was difficult, 16
may well be a very high mark.
4. Raw scores by themselves are not
very useful.
Raw scores need to be converted
into standard scores.
5. A z-score (a standard score) indicates how
many standard deviations an element is from
the mean. A z-score can be calculated from
the following formula.
z = (X - M) / SD
where z is the z-score, X is the value of the
element, M is the population mean, and SD is
the standard deviation.
6. The z-score is associated with the normal
distribution and it is a number that may be
used to:
tell you where a score lies compared with the
rest of the data, above/below mean.
compare scores from different normal
distributions
7. The Z-score is a number that may be
calculated for each data point in a set of data.
The number is continuous and may be
negative or positive, and there is no max/min
value.
The z-score tells us how "far" that data point
is from the mean. This distance from the
mean is measured in terms of standard
deviation.
8. We may make statements such as "the data
point(score) is 1 standard deviation above the
mean" and "the score is 3 standard deviations
above the mean", which means the latter
score is three times further from the mean.
9. The Mean for a set of scores is 50 while the
SD is 10.
What can we say about someone with a score
of
50?
The z-score is (50-50)/10 = 0.
Interpretation: student score is 0 distance (in
units of SD) from the mean, so the student
has scored average.
10. 60?
The z-score is (60-50)/10 = 1.
Interpretation: student has scored above
average - a distance of 1 standard deviation
above the mean.
11. 69.6?
The z-score is (69.6-50)/10 = 1.96.
Interpretation: The student has scored above
average - a distance of 1.96 above the average
score.
12. A z-score less than 0 represents an element
less than the mean.
A z-score greater than 0 represents an
element greater than the mean.
A z-score equal to 0 represents an element
equal to the mean.
13. A z-score equal to 1 represents an element
that is 1 standard deviation greater than the
mean; a z-score equal to 2, 2 standard
deviations greater than the mean; etc.
A z-score equal to -1 represents an element
that is 1 standard deviation less than the
mean; a z-score equal to -2, 2 standard
deviations less than the mean; etc.
14. If the number of elements in the set is large,
about 68% of the elements have a z-score
between -1 and 1; about 95% have a z-score
between -2 and 2; and about 99% have a z-
score between -3 and 3.