10. Find the value of range of the scores of
50 students in Mathematics achievement
test
x f
25-32 3
33-40 7
41-48 5
49-56 4
57-64 12
65-72 6
73-80 8
81-88 3
89-97 2
n=50
15. Mean Deviation
Measures the average deviation of the
values from the arithmetic mean. It
gives equal weight to the deviation of
every score in the distribution.
16. A. Mean Deviation for Ungrouped Data
MD =
Where,
MD = mean deviation value
X = individual score
= sample mean
N = number of cases
17. Steps in Solving Mean Deviation for
Ungrouped Data
1. Solve the mean value.
2. Subtract the mean value from each
score.
3. Take the absolute value of the
difference in step 2.
4. Solve the mean deviation using the
formula MD =
18. Example 1: Find the mean
deviation of the scores of
10 students in a
Mathematics test. Given
the scores: 35, 30, 26, 24,
20, 18, 18, 16, 15, 10
19.
20. Analysis:
The mean deviation of the
10 scores of students is
6.04. This means that on the
average, the value deviated
from the mean of 212 is
6.04.
21.
22. 1. Solve for the value of the mean.
2. Subtract the mean value from each midpoint or class mark.
3. Take the absolute value of each difference.
4. Multiply the absolute value and the corresponding class
frequency.
5. Find the sum of the result in step 4.
6. Solve for the mean deviation using the formula for grouped
data.
24. Analysis:
The mean deviation of the
40 scores of students is
0.63. This means that on
the average, the value
deviated from the mean
of 33.63 is 10.63.
25.
26. is the square of the standard deviation.
In short, having obtained the value of the
standard deviation, you can already
determine the value of the variance.
27. One of the most important
measures of variation.It
shows variation at the
mean.
28.
29. How to Calculate the Variance
for Ungrouped Data
1. Find the Mean.
2. Calculate the difference between
each score and the mean.
3. Square the difference between
each score and the mean.
30. How to Calculate the Variance
for Ungrouped Data
4. Add up all the squares of the
difference between each score
and the mean.
5. Divide the obtained sum by n – 1.
35. 1. Calculate the mean.
2. Get the deviations by finding the
difference of each midpoint from the
mean.
3. Square the deviations and find its
summation.
4. Substitute in the formula.
40. Standard Deviation
•Is the most important
measures of variation.
•It is also known as the
square root of the variance.
•It is the average distance of
all the scores that deviates
from the mean value.
44. 1. Solve the mean value.
2. Subtract the mean value from each score.
3. Square the difference between the mean and
each score.
4. Find the sum of step 3.
5. Solve for the population standard deviation or
sample standard deviation using the formula for
ungrouped data.
51. Steps in solving the STANDARD
DEVIATION of GROUP DATA
1. Solve the mean value.
2. Subtract the mean value from each midpoint or class
mark.
3. Square the difference between the mean value and
midpoint or class mark.
4. Multiply the squared difference and the corresponding
class frequency.
5. Find the sum of the results in step 4.
6. Solve the population standard deviation or sample
standard deviation using the formula for grouped data.