Embed Size (px)
DESCRIPTION
This was our presentation for our report in Trigonometry. Hope it can be useful for your presentations also! :)
Citation preview
MeanDeviatio
n
What is mean deviation?
The mean deviation is the first measure of dispersion that we will use that actually uses each data value in its computation. It is the mean of the distances between each value and the mean. It gives us an idea of how spread out from the center the set of values is.
How can we use mean deviation in real life?
Investments
JANUARY FEBRUARY MARCH APRIL0
20
40
60
80
100
120
WONDERLANDNEVERLANDFANTASIA
WONDERLAND = 85+85+89+95/4 = MEAN DEVIATION = 3.5
NEVERLAND = 75+75+80+85=/4 =
MEAN DEVIATION = 3.75
FANTASIA = 87+90+96+97/4=MEAN DEVIATION = 4
88.5
78.75
92.5
Formula for Mean Deviation:
(ungrouped data)
Where,μ = mean x = each
value
N = number of values
n
xMD
Mean Deviation-The mean of the distances of
each value from their mean.
Three steps on finding the mean:
1) Find the mean of all values.
2) Find the distance of each value from that mean.
3) Find the mean of those distances.
Step 2: Find the distance of each vaue from the mean.
Value Distance from 9
3 6
6 3
6 3
7 2
8 1
11 2
15 6
16 7
6+3+3+2+1 = 2+6+7
15 = 15It tells us how far, on average, all values are from the middle.
3.75
Exercises :
1) A booklet has 12 pages with the following numbers of words:
271, 354, 296, 301, 333, 326, 285, 298, 327, 316, 287 and 314
What is the mean deviation of the number of words per page?
04/13/2023
12
314287316327298285326333301296354271
309
Step 1:Find the mean.
Raw Data:271, 354, 296, 301, 333, 326, 285, 298, 327, 316,
287, 314
=
Step 2: Find the Absolute
Deviations.271354296301333326285298327316287314
384513824172411187225
x x
232 x
Step 3: Find the
Mean Deviation12
232..
N
xDM
19.33
Formula for Mean Deviation:(grouped data)
Where,μ = mean x = each value
f = frequency
f
xfMD
Three steps on finding the mean:
1) Find the mean by using the formula
2) Solve for and multiply it to the frequency of each class. Find the
3) Divide the answer of to the
f
fx
x
xf
f
Step 1: Find the mean by using the given formula:
So,
f
fxx f fx
0123456
41282121
0121664106
30f 54fx
30
54
f
fx
1.8
Step 2: Complete the table.
x f fx
0123456
41282121
0121664106
1.80.80.21.22.23.24.2
7.29.61.62.43.36.44.2
30f 54fx
x xf
6.33 xf
Step 3: Divide the answer of to the summation of
Mean Deviation =
f
12.130
6.33
f
xf
1.12
Exercises :The children in a class did a survey of the number of siblings (brothers and sisters) each of them had. The results are recorded in the following table. Calculate the mean deviation.
Step 1: Find the mean by using the given formula:
So,
f
fxx f fx
0123456789
3685421001
06161516106009
30f 78fx
30
78
f
fx
2.6
Step 2: Complete the table.
x f fx
0123456789
3685421001
06161516106009
30f 78fx
2.61.60.60.41.42.4344.45.46.4
x
7.89.64.82.05.64.83.4006.4
4.44 xf
xf
Step 3: Divide the answer of to the summation of
Mean Deviation =
f
48.130
4.44
f
xf
1.48
