Five Number Summaries 
Minimum (MinX) 
the smallest number in the data 
1st quartile (Q^{1}) 
the median of the lower half of the data 
Median (Med) 
the middle of the data 
3rd quartile (Q^{3}) 
median of the upper half of the data 
Maximum (MaxX) 
the largest number in the data 

Other Data Analysis Terms 
Mean(x̄) 
∑x / n (where n is the number of pieces in the data) 
Mode 
the number that appears the most 
Range 
the difference between the minimum and the maximum 
Standard Deviation(Sx or σx) 
1. find the mean (x̄) of the whole data set (∑x/n) 2.subtract each number from the mean and square it. 3.Find the mean of the squared differences. Your σx is the square root of the new mean. 
σx 
is standard deviation of the whole population. At the end of calculation, divide by "n" 
Sx 
standard deviation of a sample of the data. At the end of calculation, you divide it by "n1" 
Mean Absolute Deviation (MAD) 
1. Find the mean of the data 2.Find the absolute difference between each value and the mean. Then find the mean of the absolute differences 

SOCS 
Shape 
What is the shape of the graph? 
SPUGS! 
You can find the shape of the graph with a histogram of the data set 
1.Symmetric 
the graph is symmetrical 
2. Peaks 
unimodal (1 peak), bimodal (2 peaks), or multimodal (3 or more peaks) 
3. Uniform 
all of the data are the same value 
4. Gaps 
In a histogram, there is a section that has nothing. 
5. Skewness 
skewed left: the tail points left skewed right: the tail points right 

Outliers 
Are there any outliers in the data set? 
Outliers are more of a yes or no question 
find the interquartile range, from Q^{1} to Q^{3}. multiply it by 1.5 and subtract/add from the mean. That is the borderline. Anything greater than the border line is an outlier 

From now on, it will be separated based on whether or not there is an outlier or not. 
a = no outlier 
b = outlier 

Center 
What is the center of the data set? 
a 
mean 
b 
median 

Spread 
What is the spread of the data set? 
a 
Standard Deviation 
b 
IQR, range, and five number summary 


In the end, add an explanation to your data set, analyzing using all of the information 