Understanding mean and standard deviation in the normal distribution curve, Understanding scores using range, semi-interquartile range, standard deviation and variance. Converting scores through z- scores and t - scores,

1. 13Chapter
Variability
The Normal Distribution
Converted Scores
NEMA GRACE B. MEDILLO
Educ. 243 – Education Evaluation
Prof. James L. Paglinawan, Ph D.

2. Start
Variability Converted ScoresThe Normal Distribution
Chapter13

3. Variability
Variability can be defined several ways
• A quantitative distance measure based on the differences
between scores
• Describes distance of the spread of scores or distance of a
score from the mean
Purposes of Measure of Variability
• Describe the distribution
• Measure how well an individual score represents the
distribution

4. A Chart Showing the Distance
Between the Locations of Scores in
Three Distributions

5. Three Variations of the Normal Curve

6. Types of Measures of Variability
Range
Quartile Deviation
(Semi – Interquartile Range)
Standard Deviation
Variance

7. The range indicates the distance between the two most
extreme scores in a distribution
It is often unstable and can be very misleading if an
extreme score is present.
Range = highest score – lowest score

8. Compensate the sensitivity of the range by
preventing extreme scores from influencing the
computation.
It is determined by only half the scores in a
distribution.
It represents the difference between the third
quartile and the first quartile.

9. The standard deviation indicates the “average deviation” from the mean, the
consistency in the scores, and how far scores are spread out around the mean.
The deviation Score Method for
Computing the SD
𝑆𝐷 =
(𝑥 − 𝑥)2
𝑛
The Raw Score Method for
Computing the SD
𝑆𝐷 =
𝑥2 −
( 𝑥)2
𝑛
𝑛
Where,
x – raw score
𝑥 - mean score
n - number of scores in the distribution

10. The Distribution with small standard deviation
have compressed appearance and are called
homogeneous distribution.
The Distribution with large deviations have more
expanded appearance and are called heterogeneous
distribution.

11. The average of the sum of squared deviation scores
or the squared of the standard deviation.
These estimate are not very useful because they
represent squared units, not the units started with.

12. The Normal Distribution
It is a specific type of symmetrical
distribution that is mathematically
determined and has fixed properties.

13. Properties of the Normal Distribution
The mean, median, and
mode all coincide.
The percentages show
how many cases fall under
portion of the curve.

15. Using the normal curve as a model
for a distribution
mean = 61
standard deviation = 7
Difference of 7
7 points is added above the mean
7 points is subtracted below the
mean

16. 68% of the scores in the distribution fall
between 54 and 68
48% of the scores in the distribution fall
between 61 and 75

17. Concerted Scores
John obtained a score of 85 on his psychology midterm
and 90 on his history midterm.
On which test did he do better compared to the rest of
the class, if the class:
Psychology
mean = 75
sd = 10
History
mean = 190
sd = 25

18. Curves to represent the data
The shaded area represent the proportion of scores below John’s scores
84 %
2%
SD
John performance in psychology was far better than his performance in history.

19. z - Scores
• converting raw score from any distribution to a common
scale, regardless of its mean or standard deviation, so that
we can easily compare such scores.
𝑧 =
𝑥 − 𝑥
𝑠𝑑
x – the raw score
𝑥 - mean
sd – standard deviation

20. Converting John’s Raw Score Through z -
Scores
Psychology
x = 85
𝑥 = 75
sd = 10
History
x = 85
𝑥 = 75
sd = 10
𝑧 =
85 − 75
10
= + 1.0
𝑧 =
90 − 140
25
= - 2.0

21. T - Scores
• Identical with z – scores, however it does not deals with
negative numbers.
• Converting scores from z scores.
• has a mean of 50 and standard deviation of 10.
𝑇 = 10𝑧 + 50

22. John’s z – score to T - score
Psychology
z – score = + 1.0
T = 10z + 50
= 10 (1.0) + 50
= 10 + 50
= 60
History
z – score = - 2.0
T = 10z + 50
= 10 (-2.0) + 50
= (- 20) + 50
= 30

23. Relationship between z scores and T
- scores

24. Thank you…

25. Shutting down