Transcript Numbers about Numbersx

With every set of numeric
data, you can compute…
Mean
Variance
Deviations
Standard
Deviation
Square of
the
Deviations
The mean of a data set is
calculated by finding the sum of
the numbers and dividing by the
number of entries. It is also
known as the average. It is
represented by the symbol 𝑥…
Example: These are 10 Grade
Point Averages:
2.00 3.20 1.80 2.90 3.60
0.90 4.00 3.30 2.90 0.80
Find the mean…
When you
have a data
set…
1. The sum is 25.40
2. The number of
terms is 10
3. The mean is 2.54
The distance a
number is away
from the mean is
called its deviation
X
X Bar
Deviation
(X – X Bar)
2.00
2.54
-0.54
3.20
2.54
0.66
1.80
2.54
-0.74
2.90
2.54
0.36
3.60
2.54
1.06
0.90
2.54
-1.64
4.00
2.54
1.46
3.30
2.54
0.76
2.90
2.54
0.36
0.80
2.54
-1.74
X
X – X Bar
(Deviation)
(X – X Bar)²
2.00
-0.54
0.2916
3.20
0.66
0.4356
1.80
-0.74
0.5476
2.90
0.36
0.1296
3.60
1.06
1.1236
0.90
-1.64
2.6896
4.00
1.46
2.1316
3.30
0.76
0.5776
2.90
0.36
0.1296
0.80
-1.74
3.0276
Variance describes how
spread apart all of
the values are.
Since the sum of the
deviations is 0 (always),
it doesn’t make sense to
use this.
Instead, the variance
is calculated by taking
the sum of the
squared deviations and
dividing by n - 1.
(𝒙 − 𝒙)𝟐 =
𝟎. 𝟐𝟗𝟏𝟔 + 𝟎. 𝟒𝟑𝟓𝟔 + 𝟎. 𝟓𝟒𝟕𝟔 + 𝟎. 𝟏𝟐𝟗𝟔 +
𝟏. 𝟏𝟐𝟑𝟔 +𝟐. 𝟔𝟖𝟗𝟔 + 𝟐. 𝟏𝟑𝟏𝟔 + 𝟎. 𝟓𝟕𝟕𝟔 +
𝟎. 𝟏𝟐𝟗𝟔 + 𝟑. 𝟎𝟐𝟕𝟔
=11.084
The Variance (s²) =
𝟏𝟏.𝟎𝟖𝟒
𝒏−𝟏
≈1.2316
=
𝟏𝟏.𝟎𝟖𝟒
𝟗
Finally, the value
which represents
the average
distance all the
numbers are from
the mean is called
the standard
deviation. This is
the square root
of the value of
the variance.
𝑠 = 1.2316
≈ 1.1098
Going back to the original
data, we can say that the
average distance all grade
point averages are from
the mean (2.54) is
approximately 1.11 grade
points.
The closer the value of the
standard deviation is to 0,
the closer the values of the
data are to the mean.
The farther the value of the
standard deviation is from 0,
the more spread out the data
is around the mean.
Try this one…
The salaries of 8 public
school teachers:
1)
2)
3)
4)
5)
6)
7)
8)
46,098
36,259
35,084
38,617
42,690
26,202
47,169
37,109
Calculate the following
1) The mean
2)
3)
4)
5)
6)
(to the nearest hundredth)
Each deviation
(to the nearest hundredth)
The square of each
deviation (to the nearest
thousandth)
The sum of the square of
each deviation
(to the nearest thousandth)
The variance
(to the nearest thousandth)
The standard deviation
(to the nearest thousandth)
Show the steps for each
calculation.
Now continue your
calculations with
the Class Olympics
data gathered this
week with the
concepts presented
in the lesson.