Standard Deviation
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.
Normal Distribution

There are many cases where data tends to
be around a central value with no bias left or
right. This is called a Normal Distribution.

The “Bell Curve” is a Normal Distribution.

It is often called a “bell curve” because it
looks like a bell.

The Normal Distribution has
mean = median = mode.
Standard Deviation

The standard deviation is a measure of how spread out
numbers are.

Generally, this is what we find out:
68% of values are
within 1 standard
deviation of the
mean.
95% of values are
within 2 standard
deviations of the
mean.
99.7% of values are
within 3 standard
deviations of the
mean.
Learn more about Normal Distribution
and Standard Deviations

The video to play as at the bottom of the screen.
Refresher on 1, 2 and 3 standard
deviations from the mean.
IQ Scores

An IQ score is the score you get on an intelligence
test. The scores follow a normal distribution.

What percent of people have an IQ score between
85 and 115? 68%

What percent of people have an IQ score between
70 and 85? 13.5%

What percent of people have an IQ score above
130? 2.5%
0.025(300) = 7.5,
7 or 8 people in a group of 300
 In a population of 300 people, how many people
would have an IQ score greater
would you expect to have an IQ score above 130? than 130.
Standard Deviation

Example: 95% of students at school are between
1.1 m and 1.7 m tall. Assuming the data is normally
distributed, calculate the mean and standard
deviation.

The mean is halfway between 1.1m and 1.7m.

Mean = (1.1 + 1.7)/2 = 1.4 m

95% is two standard deviations either side of the
mean
(a total of 4 standard deviations) so:

1 standard deviation = (1.7 – 1.1)/4

= 0.6/4

= 0.15 m
Each interval is 0.15
below or above the
mean.
Mean
Multiply 0.15 by
2 then 3 to get
the 2nd and 3rd
intervals.