Statistics Basics
Mean - Average (symbol mue)
Mode - The Number that occurs the most
Median - Simply the center of your data after the data was ordered
Standard Deviation : is a measure of the amount of variation or dispersion of a set of values (symbol Sigma
A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set,
high standard deviation indicates that the values are spread out over a wider range.
SD is the square root of variance
SD is commonly used to measure confidence in statistical conclusions
Nth Percentiles :
The most common way to report relative standing of a number within a data set is by using percentiles.
Not Same as percentages
If your exam score is at the 90th percentile, for example, that means 90% of the people taking the exam with you scored lower than you did (it also means that 10 percent scored higher than you did.)
Interquartile Range (IQR). The IQR equals 
and reflects the distance taken up by the innermost 50% of the data. If the IQR is small, you know there is much data close to the median.
If the IQR is large, you know the data are more spread out from the median. The IQR for the test scores data set is
, which is quite large seeing as how test scores only go from 0 to 100.
Mode - The Number that occurs the most
Median - Simply the center of your data after the data was ordered
Standard Deviation : is a measure of the amount of variation or dispersion of a set of values (symbol Sigma
A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set,
high standard deviation indicates that the values are spread out over a wider range.
SD is the square root of variance
SD is commonly used to measure confidence in statistical conclusions
Nth Percentiles :
The most common way to report relative standing of a number within a data set is by using percentiles.
Not Same as percentages
If your exam score is at the 90th percentile, for example, that means 90% of the people taking the exam with you scored lower than you did (it also means that 10 percent scored higher than you did.)
FINDING A PERCENTILE
To calculate the 
percentile (where k is any number between one and one hundred), do the following steps:
percentile (where k is any number between one and one hundred), do the following steps:
1. Order all the numbers in the data set from smallest to largest.
2. Multiply k percent times the total number of numbers, n.
3.a. If your result from Step 2 is a whole number, go to Step 4. If the result from Step 2 is not a whole number, round it up to the nearest whole number and go to Step 3b.
3.b. Count the numbers in your data set from left to right (from the smallest to the largest number) until you reach the value from Step 3a. This corresponding number in your data set is the 
percentile.
percentile.
4. Count the numbers in your data set from left to right until you reach that whole number. The 
percentile is the average of that corresponding number in your data set and the next number in your data set.
percentile is the average of that corresponding number in your data set and the next number in your data set.
For example, suppose you have 25 test scores, in order from lowest to highest: 43, 54, 56, 61, 62, 66, 68, 69, 69, 70, 71, 72, 77, 78, 79, 85, 87, 88, 89, 93, 95, 96, 98, 99, 99. To find the 90th percentile for these (ordered) scores start by multiplying 90% times the total number of scores, which gives 
(Step 2). This is not a whole number; Step 3a says round up to the nearest whole number — 23 — then go to Step 3b. Counting from left to right (from the smallest to the largest number in the data set), you go until you find the 23rd number in the data set. That number is 98, and it’s the 90th percentile for this data set.
(Step 2). This is not a whole number; Step 3a says round up to the nearest whole number — 23 — then go to Step 3b. Counting from left to right (from the smallest to the largest number in the data set), you go until you find the 23rd number in the data set. That number is 98, and it’s the 90th percentile for this data set.5 Number Summary
- The minimum (smallest) number in the data set
- The 25th percentile, aka the first quartile, or Q1
- The median (or 50th percentile)
- The 75th percentile, aka the third quartile, or Q3
- The maximum (largest) number in the data set
and reflects the distance taken up by the innermost 50% of the data. If the IQR is small, you know there is much data close to the median. If the IQR is large, you know the data are more spread out from the median. The IQR for the test scores data set is
, which is quite large seeing as how test scores only go from 0 to 100.
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