Algebra 1 Common Core Student Edition, Grade 8-9

Co n cep t Byt e

Use W ith Lesson 12-3

St a n d a r d D ev i at i o n ®

Common Core State Standards

S- ID .A .2 Use st at ist ics ap p ro p riat e t o t h e... dat a

distribution to compare center... and spread ... of

two or more different data sets.

MP 2

You have learned about one measure of dispersion, range. Another measure of

dispersion is standard deviation. St a n d a r d d e v i a t i o n is a measure of how the values

in a data set vary, or deviate, from the mean.

Statisticians use several special symbols in the formula for standard deviation.

The Gr eek l et t er si g m a (a)

represents standard deviation

The cap i t al si g m a ( I ) r ep r esen t s

the sum of a series of numbers.

x is a value in the data set.

x is the mean of the data set.

n is the number of values

in the data set.

Ex a m p l e

Find the mean and standard deviation of each data

set. Which data set has a greater standard

deviation? Use tables to help organize your work.

St e p 1

St e p 2

St e p 3

St e p 4

Find the mean, x.

Find the difference between each data

value and the mean, x - x.

Square each difference, (x — x)2.

Find the average (mean) of these

2(x-x)2

squares, j,.

St e p 5 Take the square root to find the standard

deviation,

2(x-x)2

Data Set 1 Data Set 2

Xf X! X, - X, (*1 ~ * l ) 2 -*2 *2 X2 - X 2 (x2-X2)2

12.6 15 - 2. 4 5.76 13.4 14.5 -1.1 1.21

15.1 15 0.1 0.01 11.7 14.5 -2.8 7.84

11.2 15 - 3. 8 14.44 18.3 14.5 3.8 14.44

17.9 15 2.9 8.41 14.8 14.5 0.3 0.09

18.2 15 3.2 10.24 14.3 14.5 -0.2 0.04

"SA> (*i-x))2

7.772 S(*2-^ )2 4.724

n n

jfe(* 1 - X i ) 2 = 2.79 k (X2 --^ )2 *2.17

V n v n

Data set 1 has a greater standard deviation at 2.79.

Ex e r c i se s

Find the mean and standard deviation of each data set. Round to the

nearest hundredth. Which data set has a greater standard deviation?

1. Data set 1:4, 8, 5,12,3,9,5,2 2. Data set 1:102,98,103,86,101,110
   Data set 2: 5, 9,11, 4, 6, 11, 2, 7 Data set 2: 90, 89, 100, 97, 102, 97


2. Data set 1: 8.2, 11.6, 8.7, 10.6, 9.4, 10.1, 9.3 4. Data set 1: 32, 40, 35, 28, 42, 32, 44
   Data set 2:9.3,10.2, 8.1,12.3, 8.7, 9.9,10.1 Data set 2:40, 38, 51, 39, 46,40, 52

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