# Statistics/Data Analysis

by Kate Makris
# 1. Line Graph

## 1.1. Continuous Data

## 1.2. time usually marked on horizontal axis

## 1.3. Shows trends in a variable over time

## 1.4. how data values change over time

## 1.5. What the graph needs?

### 1.5.1. includes the variable or quantity that changes

1.5.1.1. Units represent data

1.5.1.1.1. Main title for graph

## 1.6. Used to see a "trend" between two variables

# 2. Scatterplot

## 2.1. relationship between two sets of data

## 2.2. What graph needs?

### 2.2.1. Main title for graph

2.2.1.1. Descriptive label that includes the variable or quantity that changes

2.2.1.1.1. Units represent data

# 3. Measure of Central Tendency- KM,LR

## 3.1. Mean

### 3.1.1. 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.

## 3.2. Median

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

## 3.3. Mode

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

## 3.4. IQR

## 3.5. Standard Deviation/Variance

### 3.5.1. 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

## 3.6. Range

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

# 4. Pictograph (RL)

## 4.1. Used to represent tellies of categories.

### 4.1.1. Categorical data

### 4.1.2. Titles

4.1.2.1. Main title for the graph that describes the given data set.

4.1.2.2. Descriptive label that includes the variable or quantity that changes.

### 4.1.3. Legend

4.1.3.1. A key that gives the symbol and shows what the symbol represents.

### 4.1.4. Link(s)

4.1.4.1. http://www.superteacherworksheets.com/pictograph.html

# 5. Dot Plot (RL)

## 5.1. Provides a quick and simple way of organizing numerical data.

## 5.2. Numerical data

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

### 5.3.1. Each x represents how many times an event occurred.

## 5.4. Outlier

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

## 5.5. Cluster

### 5.5.1. An isolated group of points.

## 5.6. Gap

### 5.6.1. A large space between data points.

## 5.7. Mode

### 5.7.1. Data value(s) that occur most often.

## 5.8. Bar Graphs

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

# 6. All the parts of a graph: (RL) http://www.beaconlearningcenter.com/weblessons/alltheparts/default.htm

# 7. Bar Graph

## 7.1. EXAMPLE

## 7.2. What is a Bar Graph used for?

## 7.3. Parts of a Bar Graph

### 7.3.1. Graph Title

### 7.3.2. Axes and their labels

7.3.2.1. Grouped Data Axis

7.3.2.2. Frequency Data Axis

### 7.3.3. Bars

## 7.4. Create your own bar graph!

# 8. Frequency Table (RL)

## 8.1. Shows how many times data occurs in a range.

## 8.2. Characteristics

### 8.2.1. Each class interval has the same size.

### 8.2.2. The size of each interval can be computed by subtracting the lower endpoint from the higher and adding 1.

8.2.2.1. Link(s)

8.2.2.1.1. http://www.psychstat.missouristate.edu/introbook/sbk07.htm

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

### 8.2.4. As the interval size increases, information is lost.

### 8.2.5. Classes (intervals) should not overlap.

## 8.3. New node

# 9. Circle Graph

## 9.1. EXAMPLE

## 9.2. What is a Circle Graph?

## 9.3. What is a Circle Graph used for?

## 9.4. Parts of a Circle Graph

### 9.4.1. Graph Title

### 9.4.2. Sectors

### 9.4.3. Sector Labels

## 9.5. Create your own Circle Graph!

# 10. Histogram

## 10.1. EXAMPLE

## 10.2. What is a Histogram?

## 10.3. What is a Histogram used for?

## 10.4. Parts of a Histogram

### 10.4.1. Graph Title

### 10.4.2. Axes and their labels

10.4.2.1. Grouped Data Axis

10.4.2.2. Frequency Data Axis

### 10.4.3. Bars

10.4.3.1. Height

10.4.3.2. Width

## 10.5. Create your own Histogram!

# 11. Abuse of Statistics (KM, AG)

## 11.1. Reported Statistics-DG

### 11.1.1. Data interpretations are only as honest as their reporters

11.1.1.1. Registered for what?

### 11.1.2. Be objective and consider all evidence provided

### 11.1.3. Question information about the responders

11.1.3.1. How were participants chosen?

11.1.3.2. How were the responses interpreted?

## 11.2. Misleading Graphs

### 11.2.1. Will be missing information

### 11.2.2. Check graphs for essential elements

11.2.2.1. Does it have a title?

11.2.2.1.1. There is no title on this graph.

11.2.2.2. Are there labels on the axes?

11.2.2.3. What is the source of the data?

11.2.2.4. Is there a key to a pictograph?

11.2.2.4.1. This graph is missing a key.

11.2.2.5. Does the pictograph use a uniform size of symbols?

11.2.2.6. Does the scale start with a zero, when applicable?

11.2.2.6.1. What are we looking at? There is a key, but no title, no axis labels.

11.2.2.7. Are the numbers on the scale equally spaced?

## 11.3. Misuse of Mean, Median, and Mode

### 11.3.1. All of these figures are considered "averages"

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

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

## 11.4. Statistics are used to display information and are commonly abused.

# 12. Stem and Leaf Plot

## 12.1. Used to show each value in a data set and group values.

## 12.2. What the graph needs?

### 12.2.1. Main title for the plot

12.2.1.1. complete number scale (stem) that accommodates the extreme values of the data set

12.2.1.1.1. Values for the "stem" written vertically from least (top) to greatest (bottom) values.

# 13. New node