This document defines and provides examples of key statistical concepts used to describe and analyze variability in data sets, including range, variance, standard deviation, coefficient of variation, quartiles, and percentiles. It explains that range is the difference between the highest and lowest values, variance is the average squared deviation from the mean, and standard deviation describes how distant scores are from the mean on average. Examples are provided to demonstrate calculating these measures from data sets and interpreting what they indicate about the spread of scores.

2. Variability- refers to the
spread of scores in the
distribution
Range
Variance
Standard Deviation

3.  the difference between the highest
value and the smallest value in the
set
Example:
Given the following sorted data, find
the range.
12, 15,19,24,24,25,26,30,35,38
R=HV-LV
R=38-12
R=26

4. Variance- it is the square of
the standard deviation
Note: The larger the variance,
the greater the variability or
the distance of scores from
the mean. The smaller the
variance, the lesser the
variability.

5. Variance of a sample
𝑠2 =
(𝑥 − 𝑥)2
𝑛 − 1
Where:
𝑠2 = variance of the set of scores
(𝑥 − 𝑥)2= sum of the squared
deviations from the mean
n = total number of classes

6. -Used to describe variability
when the mean is used to
describe the central tendency
Note: The mean is an average
of the scores in a set while the
standard deviation is a sort of
average of how distant the
individual scores are from the
mean

7. s =
(𝑥 − 𝑥)2
𝑛 − 1
Where
(𝑥 − 𝑥)- deviation from the mean
X – the original raw score
𝑥 − mean
n – total number of
observation/cases

8. Scores in a 25 item Mathematics test
23 21 19 18 18 7
15 12 10 10 8 7

9. n = 12
𝑥 = 14
s = 5.7

11. 1. The following are the
response times in seconds of
a smoke alarm after release
of smoke from a fixed source.
Find the range, variance,
and standard deviation.
12 16 12 14 19
20 10 9 15

12. 2. Twenty employees of a fast food
chain, give a course in first aid,
obtained these scores on a test
administered after the course. Find
the range, variance, and standard
deviation.
10 11 12 15 16 18 17 17 19 12
14 17 19 17 18 16 15 14 12 10

13. 3. The following are the
stopping distances, for 20
drivers at 30 miles per hour.
Find the range, variance, and
standard deviation.
69 67 56 58 70 55 70 58 70 75
72 68 80 74 61 70 61 65 58 61

14. -expressed in percentage (%)
Uses of CRV:
-For comparing distributions
measured in the same units but
which have very different
means
-For comparing distributions
measured using different units

15. 𝐶𝑅𝑉 =
𝑠
𝑥
(100)
Where
s = standard deviation
𝑥 = mean
Note: the final answer is always
expressed in percent form

16. The weight of the girls in Grade
8 students are as follows. Find
CRV.
37 40 47 30 37 20 48
48 49 50 36 35 28 39

18. Determines the position of a
single value in relation to other
values in a sample or
population data set

19. Quartile
Interquartile
Percentile
Z-score

20. Divides a ranked data set into four
equal parts
3 measures in the quartile:
- First quartile (𝑄1)
- Second quartile (𝑄2)
- Third quartile (𝑄3)

21. Lower quartile
25% of the data
(lower 25%)

22. Median Quartile
50% of the data falls on 𝑄2

23. Upper Quartile or the upper
75%

24. Given the following set of measurements of
the grade point average of a Biology class
during the second grading period. Find the
quartiles
1.5 1.8 2.1 2.4 2.9
1.2 1.9 2.1 2.5 3
1.5 1.9 2.2 2.8 3
1.5 2 2.3 2.8 3.1

25. Measures the relative
standing of a particular
measurement in a data set.