Summary Statistics
stat
Vehicle Year
Right skewed
What is the equation of a z score?
Z Score = (value - average) / standard deviation
What is standard deviation?
How spread out a list of numbers are
Which number do we use for standard deviation on the calculator?
Sx or σx
Sx
Winning powerball numbers
Uniform
Each number is equally likely
The z scores for the height of several people are listed below.
Bob: -1.2
Sally: 2.4
Dave: 0.1
Who was the tallest?
Sally
The higher the z score, the higher the height.
The price of 30 drinks ordered at Starbucks was recorded.
What units will the standard deviation be in?
Dollars
Ex) Standard Deviation = 1.5 Dollars
What is the range of the following numbers?
0, 25, 10, 8, 3
25
Range = max - min = 25 - 0 = 25
Retirement age
https://www.researchgate.net/figure/Distribution-of-retirement-age-in-our-sample_fig4_342989103
Left skewed
The z scores of several student's grade on an exam are listed below.
Bob: 0.5
Sally: -1.5
Dave: -0.2
Which student scored closest to the average exam grade?
Dave
The closer the z score is to zero, the closer the value is to the average
Will the salaries of all FSU employees have a low or high standard deviation?
High.
Low salaries for janitors and restaurant workers.
High salaries for famous professors.
Several numbers as well as the lower and upper fence are listed below.
Values = -30, 10, 25, 8, 2
Lower Fence = -5
Upper Fence = 21
Are any values outliers?
-30
An outlier will be less than the lower fence or greater than the upper fence.
-30 is less than the upper fence of -5.
For a left or right skewed dataset, which number should you use to represent the typical value?
Mean or median
Median
The z scores for the salary of professors at FSU are listed below.
Steve: 0.3
Mark: -1.3
Alexandra: 4.6
Could any of these professors be an outlier?
Alexandra is probably an outlier
Any z score that is less than -3 or greater than 3 is probably an outlier.
Will the salaries of all the teaching assistants in a single department have a low or high standard deviation?
Low
All teaching assistants are paid almost the same.
What is the equation for IQR?
75th Percentile - 25th Percentile
or
Q3 - Q1
For a bell shaped or uniform distribution, which metric should you use to represent the typical value?
Mean or median
Mean
The average and median will be very close to one another. The average, however, is more likely to be understood by people.
Mark has a height z score of 2.
The standard deviation of height was 0.5 feet.
How much taller was Mark than the average?
1 foot
Distance from average = z score * standard deviation = 2 * 0.5 = 1
What would the standard deviation be of the following 5 numbers?
8, 8, 8, 8, 8
Zero
If all the numbers are the same, there is no spread so the standard deviation is zero.