1. Foundations of Math I: Unit 3 - Statistics
Measures of Central Tendency: numbers that represent the middle
Mean ( x ):
Arithmetic average
Median:
Middle of the data listed in ascending order
(use if there is an outlier)
Mode:
Most common number (can be more than one number or no numbers)
Foundations of Math 3: Unit 3

2. Foundations of Math I: Unit 3 - Statistics
Measures of Spread: Standard Deviation
Measure of variation or distance from mean value.
Standard Deviation (σx, Sx):
Range:
Difference between the Maximum and Minimum
Quartiles:
Separates ascending data into 4 equally sized(25%)
groups based on the how many data values
Inner Quartile Range (IQR):
Difference between 3rd and 1st Quartiles (Middle 50% of data)

3. 5 Number Summary: Min: Q1: Med: Q3: Max: Minimum Value (0 Percentile)
Quartile 1 (25th Percentile)
Med:
Median (50th Percentile)
Q3:
Quartile 3 (75th Percentile)
Max:
Maximum or Q4 (100th Percentile)
Five Number Summary is always listed in ascending order Minimum to Maximum
Additional Calculations using the 5-Number Summary
Range:
Max – Min
IQR:
Q3 – Q1
Foundations of Math 3: Unit 3

4. 5 Number Summary: Examples
The following is the 5-number summary of data:
2.72, 3.12, 3.31, 3.67, 3.89
What is the Q1?
What is the Q3?
What is the Range?
The following numbers are from a 5-number summary of data:
35, 85, 65, 70, 90
What is the Median?
What is the Range?
What is the IQR?
The following numbers are from a 5-number summary of data:
86.5, 97.7, 86.09, 72.9, 94.1
What is the Median?
What is the Range?
What is the IQR?
Foundations of Math 3: Unit 3

5. REQUIRED Statistics by Hand!
Calculator Commands: One Variable Statistics
Input Data: [STAT]  [EDIT]  L1
DO NOT DELETE Lists: Highlight L1  [Clear] to start new list of data
Get Statistics from Data: [STAT]  [CALC]  [1: 1-Var STATS]  [ENTER]
Minimum
1st Quartile
Median
3rd Quartile
Maximum
Mean
Standard
Deviation
REQUIRED Statistics by Hand!
Identify the MODE by looking for the most common number(s)
Use Five-Number Summary to calculate
IQR with Q3 and Q1
RANGE with maximum and minimum

6. Example #1: Listed below are the weights of 10 people (in lbs)
225, 180, 195, 155, 124, 146, 183, 117, 130, 155
Minimum: _________
1st quartile: _________
Median: _________
3rd quartile: _________
Maximum: _________
Use the graphing calculator to find:
Mean: __________________
Standard Deviation: _____________
Find the following statistics based on the data and calculator information:
Mode: ______________ Range: _____________ IQR: _______
Write the numbers in ascending order:

7. PRACTICE: Find the mean and standard deviation
#1: The following is the amount of black M&M’s in a bag: 12, 13, 14, 15, 15, 16, 17, 20, 21, 22, 23, 24, 25
#2: The following is the amount of red Skittles in a bag:
9, 10, 11, 14, 15, 16, 17, 20, 21, 23, 26, 27, 28
[Default]
[MC Any]
[MC All]
#3: Explain why the means are the same.
You can add different numbers and still get the same total to have the same average.

8. Find the 5 number summary using the calculator.
PRACTICE FIVE-NUMBER SUMMARY:
Find the 5 number summary using the calculator.
Gia:
8, 9, 9, 9, 6, 9, 8, 6, 8, 6, 8, 8, 8, 6, 6, 6, 3, 8, 8, 9
Maria:
8, 9, 6, 7, 9, 8, 8, 6, 9, 9, 8, 7, 8, 7, 9, 9, 7, 7, 8, 9
Min: __________
Min: __________
Q1: __________
Q1: __________
Median: __________
Median: __________
Q3: __________
Q3: __________
Max: __________
Max: __________
Calculate:
Range: _________
Interquartile Range: ______
Calculate:
Range: _________
Interquartile Range: ______
Foundations of Math 3: Unit 3