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# Statistics/Data Analysis

## Line Graph

### What the graph needs?

includes the variable or quantity that changes, Units represent data, Main title for graph

## Scatterplot

### What graph needs?

Main title for graph, Descriptive label that includes the variable or quantity that changes, Units represent data

## Measure of Central Tendency- KM,LR

### Mean

Add all the numbers then divide by the number of numbers. Example- In a set of numbers {20, 22, 22, 23, 24} the mean is 22 after rounding.

### Median

The middle number from least to greatest. Example- In a set of numbers {20, 22, 22, 23, 24} the median is 22.

### Mode

Numbers that occur the most often. Example- In a set of numbers {20, 22, 22, 23, 24} the mode is 22.

### Standard Deviation/Variance

The Standard Deviation is a measure of how spread out numbers are. Its symbol is σ (the Greek letter sigma) The formula is easy: it is the square root of the Variance. The average of the squared differences from the Mean. Example- 20,22,22,23,24/5 = Avg of 22.2 then subtract this with all the numbers and square it then divide this by how many numbers there is. It will look like this. 4.84+.04+.04+.04+.64+3.24=8.8/5 At last you find the square root to get the variance. So the final answer would be 1.32

### Range

Biggest number subtracted by the smallest number. Example- In a set of numbers {20, 22, 22, 23, 24} the range is 24-20= 4

## Pictograph (RL)

### Used to represent tellies of categories.

Categorical data

Titles, Main title for the graph that describes the given data set., Descriptive label that includes the variable or quantity that changes.

Legend, A key that gives the symbol and shows what the symbol represents.

## Dot Plot (RL)

### A horizontal number line on which each score is represented by a dot, or an x above the corresponding number-line value

Each x represents how many times an event occurred.

### Outlier

A data point whose value is significantly greater than or less than other values.

### Cluster

An isolated group of points.

### Gap

A large space between data points.

### Mode

Data value(s) that occur most often.

### Bar Graphs

Shading in a dot plot in the squares of a grid paper and adding a vertical axis depicting the scale forms a bar graph.

## Frequency Table (RL)

### Characteristics

Each class interval has the same size.

The size of each interval can be computed by subtracting the lower endpoint from the higher and adding 1., Link(s), http://www.psychstat.missouristate.edu/introbook/sbk07.htm

The number of data values are known but the particular data values are unknown.

As the interval size increases, information is lost.

Classes (intervals) should not overlap.

## Bar Graph

Daniel Gomez

### What is a Bar Graph used for?

(Categorical Data) To compare numbers of data items in grouped categories; order of data does not matter except for convenience.

### Parts of a Bar Graph

Graph Title

Axes and their labels, Grouped Data Axis, Frequency Data Axis

Bars

## Circle Graph

Daniel Gomez

### What is a Circle Graph?

A graph which consists of a circular region partitioned into disjoint sections, with each section representing a part or piece of the whole.

### What is a Circle Graph used for?

(Categorical Data) To show the division of a whole into parts.

Graph Title

Sectors

Sector Labels

## Histogram

Daniel Gomez

### What is a Histogram?

A diagram consisting of rectangles whose area is proportional to the frequency of a variable and whose width is equal to the class interval.

### What is a Histogram used for?

(Numerical Data) To compare numbers of data items grouped in numerical intervals; order matters in the data depicted.

### Parts of a Histogram

Graph Title

Axes and their labels, Grouped Data Axis, Frequency Data Axis

Bars, Height, Width

## Abuse of Statistics (KM, AG)

### Reported Statistics-DG

Data interpretations are only as honest as their reporters, Registered for what?

Be objective and consider all evidence provided

Question information about the responders, How were participants chosen?, How were the responses interpreted?

Will be missing information

Check graphs for essential elements, Does it have a title?, There is no title on this graph., Are there labels on the axes?, What is the source of the data?, Is there a key to a pictograph?, This graph is missing a key., No key, Does the pictograph use a uniform size of symbols?, Does the scale start with a zero, when applicable?, What are we looking at? There is a key, but no title, no axis labels., Are the numbers on the scale equally spaced?

### Misuse of Mean, Median, and Mode

All of these figures are considered "averages"

These figures can be reported to suit the statistician's needs

Watch for a low number of contributors, which would allow an extremely high or low value skew the overall data

## Stem and Leaf Plot

### What the graph needs?

Main title for the plot, complete number scale (stem) that accommodates the extreme values of the data set, Values for the "stem" written vertically from least (top) to greatest (bottom) values., a key or legend