Statistics
3.1 Descriptive Statistics
I.
Two important ideas
A. What is typical value of set
B. How spread out values are
3.1.1. Range, Quartile, and IQR
I. Mean: the value each data point would have if all data points were equal
A.
II.
III.
IV.
3.1.2.
I.
II.
III.
𝑠𝑢𝑚 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑣𝑎𝑙𝑢𝑒𝑠
B. Outlier: a value that is significantly different from rest of data set
1. Impact: contribute more to total than data points closer to overall group
Median: the value with same number of data points above as below value
A. Odd number of values: middle value
B. Even number of values: median of middle two values
C. Values must be organized from smallest to largest
D. Mean vs. median
1. Mean close to median: data fairly evenly distributed
2. Mean > median: data skewed above median
3. Mean < median: data skewed below median
Mode: the value that occurs most frequently
A. Bimodal: two different data values each occur most frequently
Measure of central tendency
A. Often reported together to provide more complete picture
B. Mean and median of finite arithmetic sequence always equal
1. Proof: pg. 86, ex. 3.1.d.
2. Give info about representative value
3. Attempt to communicate info about center of data
Range, Quartile, and IQR
Range: difference between largest and smallest value in data set
A. Rough guideline for spread of data
1. Differentiate between two different data sets with same mean, median, and mode
B. Several problems
1. Easily affected by outliers
2. Must be reported with mean to be properly interpreted
Quartiles
A. Lower/first quartile: median value of data below the median in set
B. Upper/third quartile: median value of data above the median in set
C. Upper, lower quartiles and median separate data into four equal parts
Interquartile range (IQR): different between lower and upper quartile
A. IQR test for outliers
1. 𝑣𝑎𝑙𝑢𝑒 > 𝑢𝑝𝑝𝑒𝑟 𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 + (1.5) × (𝐼𝑄𝑅)
2. 𝑣𝑎𝑙𝑢𝑒 < 𝑙𝑜𝑤𝑒𝑟 𝑞𝑢𝑎𝑟𝑡𝑖𝑙𝑒 − (1.5) × (𝐼𝑄𝑅)