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Types of Charts or Graphs

...

Frequency Polygon

X axis = score, Y axis = frequency, type of line graph that shows frequency distributions. Uses mid-point to plot connect back to axis.

Bar Graph

A graph that uses horizontal or vertical bars to display countable data

Time Series

construct with time (Jan, Feb, March) on x axis

and values oi y axis

and values oi y axis

Frequency Histogram

Construct using rectangles that are the same width and touch each other. Heights of the bars represent observed frequencies. If large amounts of data using classes, use lower class limits on x axis.

Different types of histograms

Same as frequency histogram but uses specific frequency values. Ex. Relative Frequency, Cumulative Frequency, Cumulative Relative Frequency.

Pie Chart

construct using relative frequency and multiply by 360 to get angle on pie chart

Ogive

Point chart based off of cumulative frequency. Plots upper limit of each class. Does not connect to axis. * Relative ogive uses relative frequency values

Symbols

...

∑

summation

μ

population mean

add all values of population and divide by number of values

add all values of population and divide by number of values

xbar

Sample Mean

add all values of sample and divide by number of values

...................∑xi fi

xbar=..........-------

....................∑ fi

add all values of sample and divide by number of values

...................∑xi fi

xbar=..........-------

....................∑ fi

N

Size of population

n

Size of sample

i

values of μ (population) or x-bar (sample) individual values

M

median value in middle when arranged in ascending order

If there are odd number of values there will be two middle values. Add the two middle values and divide by 2.

If there are odd number of values there will be two middle values. Add the two middle values and divide by 2.

R

range

Largest number minus smallest number to get range

not resistant

Largest number minus smallest number to get range

not resistant

...2

s

s

Sample Variance of raw data not in classes, needs 4 columns

s2= ∑(x -xbar) 2(squared)

..................----------------

......................... n-1

same formula expanded

s2= (X1-xbar)2 +(X2-xbar)2+(X3-xbar)2

........-------------------------------------------

......................... n-1

s2= ∑(x -xbar) 2(squared)

..................----------------

......................... n-1

same formula expanded

s2= (X1-xbar)2 +(X2-xbar)2+(X3-xbar)2

........-------------------------------------------

......................... n-1

s

Sample standard variation

not resistant

not resistant

...2

s

s

Sample Variance of data in classes, needs 8 columns

...2

σ

σ

Population Variance

Population Variance of raw data not in classes, needs 4 columns

σ 2= ∑(x -μ) 2(squared)

___________________

.................N

σ 2= (X1-μ)2 +(X2-μ)2+(X3-μ)2

__________________________

................N

not resistant

Population Variance of raw data not in classes, needs 4 columns

σ 2= ∑(x -μ) 2(squared)

___________________

.................N

σ 2= (X1-μ)2 +(X2-μ)2+(X3-μ)2

__________________________

................N

not resistant

...2

s

s

..., population standard deviation

σ = √ σ2

not resistant

σ = √ σ2

not resistant

...2

σ

σ

Population Variance of data in classes, needs 8 columns

f

frequency or fences

IQR

Inter Quartile Range - the middle 50% , resistant

use this if data is skewed left or right better measure of dispersion

use this if data is skewed left or right better measure of dispersion

Q2=

Median

z

z score

x- mean(either xbar or μ)

----------------------------------

Standard deviation (either σ or s)

x- mean(either xbar or μ)

----------------------------------

Standard deviation (either σ or s)

xbar w

weighted mean

.................∑wi x

XBAR w= ---------

...................∑w

.................∑wi x

XBAR w= ---------

...................∑w

Pk

kth percentile are < or equal to value data

ex. P1=1%, P2=2%.....P99=99%

ex. P1=1%, P2=2%.....P99=99%

Definitions

...

Mean average

The sum of the numbers in a data set divided by the number of items in the data set.

Median

Middle number in a set of numbers that are listed in order

Mode

the most frequent value occurring in a data set

* The mode is the only method used with non value (ex color) for central tenancy

* The mode is the only method used with non value (ex color) for central tenancy

When a bell shaped chart is skewed Left

mean< median

When a bell shaped chart is skewed Right

mean>median

When a bell shaped chart is symmetric

mean=median

Cumulative Frequency

a running total of frequencies

ex. First value is constant

2nd value is sum of 1st and 2nd value

3rd value is sum of 1st, 2nd and 3rd value.

ex. First value is constant

2nd value is sum of 1st and 2nd value

3rd value is sum of 1st, 2nd and 3rd value.

Cumulative Relative Frequency

a running total of relative frequencies

ex. First value is constant

2nd value is sum of 1st and 2nd value

3rd value is sum of 1st, 2nd and 3rd value.

ex. First value is constant

2nd value is sum of 1st and 2nd value

3rd value is sum of 1st, 2nd and 3rd value.

Frequency

How many times something occurs, the number of observations in a given statistical category,

Relative Frequency

Individual frequency divided by the sum of all frequencies.

The ratio of the number of observations in a statistical category to the total number of observations.

The ratio of the number of observations in a statistical category to the total number of observations.

Deviation

deviation = Xi- μ or Xi- xbar

summations of all deviations should equal 0

summations of all deviations should equal 0

Discrete

You can count the values

Continuous

Infinite number of possible values NOT countable

Empirical Rule

Bell shaped distribution

~68% of data will be in 1st deviation (μ +/- 1σ)

~95% of data will be in 2nd deviation (μ +/- 2σ)

~99.7% of data will be in 3rd deviation (μ +/- 3σ)

~68% of data will be in 1st deviation (μ +/- 1σ)

~95% of data will be in 2nd deviation (μ +/- 2σ)

~99.7% of data will be in 3rd deviation (μ +/- 3σ)

fences

cutoff point for determining outliers

Lower Fence

Q1 - 1.5(IQR)

Upper Fence

Q3 + 1.5(IQR)

outliers

extreme observations