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### 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.

### 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.

### 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

### xbar

Sample Mean

add all values of sample and divide by number of values

...................∑xi fi

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

....................∑ fi

### 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.

###
...2

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

###
...2

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

### IQR

Inter Quartile Range - the middle 50% , resistant

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

### z

z score

x- mean(either xbar or μ)

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

Standard deviation (either σ or s)

### 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

### 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.

### 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.

### 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.

### 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)