Calculate
Standard Deviation
ANALYZE THE SPREAD OF DATA.
Focus 6 Learning Goal – (HS.S-ID.A.1, HS.S-ID.A.2, HS.S-ID.A.3, HS.S-ID.B.5) =
Students will summarize, represent and interpret data on a single
count or measurement variable.
4
In addition to level
3.0 and above and
beyond what was
taught in class, the
student may:
· Make connection
with other concepts
in math
· Make connection
with other content
areas.
3
The student will summarize,
represent, and interpret data
on a single count or
measurement variable.
- Comparing data includes
analyzing center of data
(mean/median), interquartile
range, shape distribution of a
graph, standard deviation
and the effect of outliers on
the data set.
- Read, interpret and write
summaries of two-way
frequency tables which
includes calculating joint,
marginal and relative
frequencies.
2
1
The student will be
able to:
- Make dot plots,
histograms, box
plots and two-way
frequency tables.
- Calculate
standard deviation.
- Identify normal
distribution of data
(bell curve) and
convey what it
means.
With help from
the
teacher, the
student has
partial success
with summarizing
and interpreting
data displayed in
a dot plot,
histogram, box
plot or frequency
table.
0
Even with
help, the
student has
no success
understandin
g statistical
data.
Standard Deviation

Standard Deviation is a measure of how spread
out numbers are in a data set.

It is denoted by σ (sigma).

Mean and standard deviation are most
frequently used when the distribution of data
follows a bell curve (normal distribution).
Formula for Standard Deviation
𝜎



=
𝑥−𝑥
𝑛 −1
2
Here is what each part of the formula means:
𝑇ℎ𝑖𝑠 𝑖𝑠 𝑡ℎ𝑒 𝑠𝑢𝑚 𝑠𝑦𝑚𝑏𝑜𝑙. 𝐼𝑡 𝑚𝑒𝑎𝑛𝑠 𝑡𝑜 𝑎𝑑𝑑 𝑢𝑝 𝑤ℎ𝑎𝑡 𝑓𝑜𝑙𝑙𝑜𝑤𝑠.
x is each data item in the data set.
 𝑥 is the mean of the data set.

Basically the numerator states to subtract the mean from each
number in the data set and square it. Then add them all up.

The “n” in the denominator is the total number of values you
have.
Calculate the standard deviation of
the data set: 60, 56, 58, 60, 61
1.
Calculate the mean 𝑥.
1.
2.
𝝈=
Compute the variance which is (x – 59)2.
1.
(60 – 59)2 = 1
2.
(56 – 59)2 = 9
3.
(58 –
4.
(60 – 59)2 = 1
5.
3.
(60 + 56 + 58 + 60 + 61) ÷ 5 = 59
(61 –
59)2
59)2
=1
=4
Add up the variance.
1.
1 + 9 + 1 + 1 + 4 = 16
𝒙 − 𝒙
𝒏 −𝟏
𝟐
4. Divide the variance by (n – 1).
1. n = 5
2. 5 – 1 = 4
3. 16 ÷ 4 = 4
5. Square root that answer.
1.
4=𝟐
6. σ = 2 This means the standard
deviation is 2.
Measures of Deviation Practice
(Each student needs a copy of the activity.)
 The
data set below gives the prices (in
dollars) of phones at an electronic
store.
 35,
50, 60, 60, 75, 65, 80
 Calculate
 (35
the mean ( 𝑥 ):
+ 50 + 60 + 60 + 75 + 65 + 80) ÷ 7
 60.71
𝝈=
𝒙 − 𝒙
𝒏 −𝟏
𝟐
Measures of Deviation Practice

Use the table to help calculate the
variance (𝑥 − 𝑥)2. (Round all values to the nearest
hundredth.)
𝝈=
(35 – 60.71) = -25.71
661.00
(50 – 60.71) = -10.71
114.70
(60 – 60.71) = -0.71
0.50
(60 – 60.71) = -0.71
0.50
(75 – 60.71) = 14.29
204.20
(65 – 60.71) = 4.29
18.40
(80 – 60.71) = 19.29
372.10
1,371.40
𝒙 − 𝒙
𝒏 −𝟏
𝟐
Measures of Deviation Practice


Divide the sum of the squared deviations by (n – 1).

n=7

7–1=6

1371.4 ÷ 6 =

228.57
Square root your answer :



228.57 =
15.12
The standard deviation (σ) is 15.12.
Explain what the mean and standard
deviation mean in the context of the
problem.
A typical phone at the electronics store
costs about $60.71. However, 68% of the
phones will be $15.12 lower and higher
than that price. ($45.59 – $75.83)