Variance & Standard Deviation

Range

The difference between the maximum and
minimum data entries in the set. The data must be quantitative.

Deviation

The difference between the data entry, x, and
the mean of the data set.

Variance

How far a set of numbers is spread out

Standard Deviation

Shows how much variation from the average exists.

Standard Deviation for Grouped Data

When a frequency distribution has classes,
estimate the sample mean and the sample
standard deviation by using the midpoint of each class.

Chebyshev's Theorem

The portion of any data set lying within k standard deviations
(k > 1) of the mean is at least. k represents the number of standard deviations from the mean.(is used when the distribution is not bell-shaped or not known. It gives the minimum percent of data values that fall within the given number of SD of the mean.)

find the data value given the
standard deviation and the mean
use the formula

μ - kσ

Coefficient of variation

describes the standard deviation as a percent of the mean.(Because it has no units, you can use the coefficient of variation to compare data with different units.) CV=standard deviation/mean * 100

symmetric and unimodal graph

When a distribution is symmetric and unimodal
the mean, median and mode are equal

uniform graph

When a distribution is uniform it is also symmetric.
There is no mode.

skewed left graph

The mean is to the left of the
median.

skewed right graph

The mean is to the right of the median.

A measure of central tendency

A value that represents a typical, or central,
entry of a data set.(Mean, Median, Mode)

Mean

The sum of all the data entries divided by
the number of entries. (μ=Σx/N)

- μ
-Σx
- N
-(x bar)
-n

-Greek letter mu (mew)
-Sum of all of the data entries (x) in the data set.
-the number of entries in a population
-(x bar)
-the number of entries in a sample

Median

The value that lies in the middle of the data
when the data set is ordered.(odd number of entries: median is the middle data entry. even number of entries: median
is the mean of the two middle data entries).

Mode

The data entry that occurs with the greatest
frequency. (repeats)

how to do Grouped chart

Xm(L2): midpoint
-XmF(L3): L1 * L2
-Xm- x bar(L4): midpoints - means
-(Xm-x bar)^2(L5): square root your answer from L4
-(L6): square root L4 times freq

Mean in grouped chart

Xmf total/ F total

how to find Variance

(Xm-x bar)^2/f-1

at least 88.9%
At least 75%

x-3s and x+3s
x-2s and x+2s

-S

-s squard 2

-o 2

-sample standard deviation

- sample variance

-population variance

fences

marked places on either side of the box to represent various portions of the data. Any number lower or higher thanthe fences are the outliers.

how to find fences

Lower fences: Q1 - 1.5 x(IQR)

Upper fences: Q3 +1.5 x (IQR)

Box-and-Whisker Plot

It is an exploratory data analysis tool. Highlights important features of a data set.

IQR

how to find it

-Interquartile range of a data set is the differences between the third and first quartiles

-Q3-Q1