Mean

Measures of Center

Mean from Distribution

Definition:

measure of central tendency of a given distribution

Formula:

Mean = [((Max + Min)/2) x Frequency]/ total # Frequencies

Range

The range is the difference between the maximum and minimum values

(Max - Min = Range)

The range includes outliers which makes it not as useful of a measurement

Range Rule of Thumb

Used to estimate the standard deviation from sample data

Formula:

Also: (maximum-minimum)/4

Standard Deviation

V

a

r

i

a

n

c

e

Definition: a value that is computed by dividing the sum of a set of terms by the number of terms

Median

Definition: the middle value in a series of values arranged from smallest to largest

Mode

Definition: the most frequent value of a set of data

Midrange

What is it?

Definition: the value midway between the maximum and minimum values in the original data set

Standard deviation is the measure of variation of all values from the mean

Formula =

About

1) Add Min+Max/2

a. (11+15)/2=13

b. (16+20)/2=18

c. (21+25/2=23

d. (26+30)/2=28

e. (31+35)/2=33

f. (36+40)/2=38

g. (41+45)/2=43

h. (46+50)/2=48

Skewedness

Most values of standard deviation are positive (it will be zero only when the data values are all the same number)

The units of standard deviation are the same as the original data values

The larger the standard deviation, the larger the variation

definition: distribution of data is not symmetric and extends more to one side than the other

2) Take the mean of each range found and multiply by frequency

13*2=26

18*3=54

23*3=69

28*5=140

33*6=198

35*6=210

43*3=129

48*2=96

Example:

How to & Example

Add these sums and divide by the total # of

frequencies

13*2=26

18*3=54

23*3=69

28*5=140

33*6=198

35*6=210

43*3=129

48*2=96

=922

922/30

= 30.73

Minimum : 7

Maximum: 19

So...

Standard deviation= (19-7)/4

= 12/4

s= 3

Find the standard deviation of values: 2, 9, 10

Minimum and Maximum

"Usual" Values

1. Find the mean of the values

2 + 9 + 10 / 3

2. Subtract each value from the mean

2-7= -5

9-7= 2

10-7= 3

3. Square each subtracted value

To find the maximum and minimum usual values, you need the mean and the standard deviation

Formulas: "Maximum usual"= mean+ 2(st. deviation)

"Minimum usual"= mean- 2(st. deviation)

4. Add the values that were squared

5. Square root the sum by n-1 (n= the number of values)

Example

Find the maximum and minimum usual values given that the mean is 20 and the standard deviation is 2.

Maximum= 20 + 2(2)

20+4

Maximum usual value is 24.

Minimum= 20 - 2(2)

20-4

Minimum usual value is 16.

Variance= a measure of the variation equal to the square of standard deviation

it can never be negative

Ex. 2, 9, 10

Range= 10-2 = 8

Ex. Using the standard deviation found in the previous example --> (4.36)2 = 19.0

Example: 1,2,3,4,5

mean= (1+2+3+4+5)/5

= 15/5

mean= 3

**Chapter 3 Sections 2 & 3**

Example: 1,2,3,4,5

1 2 3 4 5

Median is 3 .

/ / / /

Example: 1,2,3,

4

,

4

,5,

Mode is 4.

Example: 1,2,3,6,19

Midrange= (19-1)/2

= 18/2

Midrange= 9