Mean, Median, Mode, and Range
The _____________ is calculated as the largest value minus the smallest value.
Which number is NOT part of the five-number summary?
Median
Mode
Maximum
Minimum
2. Mode
3,2,3,3,5,6,1,6,29
is there an outlier in this data? If so, what is it?
yes, 29
What are the steps to find the MAD of a set of data?
1. Find the mean of the data
2. Find the distance of each point from the mean
3. Find the mean of the distances. This is your MAD
Is this a statistical Question?
What is the most popular car color in the school parking lot?
Yes
Which measure would you use to describe the most typical (happening most often) value in a list?
A. Range
B. Mean
C. Mode
D. Median
C. Mode
In a box plot, the box shows:
All data values from minimum to maximum
The middle 50% of the data
Only the outliers
The mean and standard deviation
2. The middle 50% of the data
3,2,3,3,5,6,1,6,29
What would be the better measure of center for this set of data? (Mean or Median?)
Median
Can your distances from your points to your mean be written as negative numbers?
No
Is this a Statistical Question?
What is the temperature at noon at City Hall?
No
The data set: 4, 6, 9, 11, 14, 20. What is the median?
A. 9
B. 10
C. 11
D. 12
B. 10
Which of these correctly orders the five-number summary from smallest to largest?
Q3, median, Q1, minimum, maximum
Minimum, Q1, median, Q3, maximum
Median, minimum, Q1, Q3, maximum
Minimum, median, Q1, Q3, maximum
2. Minimum, Q1, median, Q3, maximum
3,2,3,3,5,6,1,6,29
What would be the better measure of variabilty (MAD or IQR?) for this data?
IQR
Find the MAD of this data
1,4,2,5
Mean = 3
Distance = 2,1,1,2 = 6
Mean of Distance = 6/4 =1.5
MAD = 1.5
Is this a Statistical Question?
How many hours did I sleep last night?
No
The test scores in a class are: 60, 75, 75, 80, 95. Describe the mode and the range, and explain what each tells you about the scores.
Mode - 75
Range - 35
75 is the most common test score and the scores vary by 35 points
A class recorded the number of books read in a month by each student: 2, 3, 3, 4, 6, 8, 9.
Find the five-number summary
Minimum = 2
Q1 = 3 (median of the lower half 2,3,3 is 3)
Median = 4 (middle value of the whole list)
Q3 = 8 (median of the upper half 6,8,9 is 8)
Maximum = 9
What are the options to use for Measure of Center? When should you use one vs. the other?
Mean or Median
Ues mean if data is symmetrical and has no outliers. Use Median if data is skewed or has outliers
Find the MAD of this data
5,16,20,18,1
Mean = 12
Distance = 7,4,8,6,11 = 36
Mean of Distance = 36/5 = 7.2
MAD = 7.2
Is this a Statistical Question?
How many pets does each 6th grader have?
Yes
Explain a situation where the median is a better measure than the mean for describing typical values.
If the data has Outliers, is skewed, etc.
How can box plots help you compare two sets of data? Give one clear example of a comparison you could make with box plots.
Answers may vary
What are the options for measure of variabilty?
When is one better to use than the other?
MAD and IQR
MAD is better if you used Mean for measure of center, data is symmetrical, and spread out.
IQR is better if you used median for measure of center, data is skewed, or close together.
Find where the student went wrong finding the MAD of the data
Data: 100, 54, 88, 63
Mean: 100+54+88+63= 305
Distances from the mean = 205, 251, 217, 242
Mean of the Distances = 205+251+217+242=915 915/4 = 228.75
MAD = 228.75
The Mean was not divided by 4. It should be
305/4 = 76.25.
What is the difference between a Statistical and NonStatistical Question?
Statistical: Answers require collecting, organizing, and analyzing varied data.
Non-Statistical: Answer is a specific fact or single number.