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Informal Statistics Project

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Jags Sharma

on 13 April 2016

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Transcript of Informal Statistics Project


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
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