Foundations of Math I: Unit 3 - StatisticsMeasures of Central Tendency: numbers that represent the middle
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)
Mean ( x ):
Foundations of Math I: Unit 3 - Statistics
Standard Deviation (σx, Sx): Measure of variation or distance from mean value.
Measures of Spread: Standard Deviation
Range: Difference between the Maximum and Minimum
Inner Quartile Range (IQR):Difference between 3rd and 1st Quartiles (Middle 50% of data)
Quartiles: Separates ascending data into 4 equally sized(25%) groups based on the how many data values
5 Number Summary:Minimum Value (0 Percentile)
Q1: Quartile 1 (25th Percentile)
Med: Median (50th Percentile)
Min:
Q3: Quartile 3 (75th Percentile)
Max: Maximum or Q4 (100th Percentile)
IQR:Q3 – Q1Range: Max – Min
Additional Calculations using the 5-Number Summary
Five Number Summary is always listed in ascending order Minimum to Maximum
5 Number Summary: Examples
The following numbers are from a 5-number summary of data:35, 85, 65, 70, 90
a. What is the Median?b. What is the Range?c. What is the IQR?
The following is the 5-number summary of data:2.72, 3.12, 3.31, 3.67, 3.89
a. What is the Q1?b. What is the Q3?c. What is the Range?
The following numbers are from a 5-number summary of data:86.5, 97.7, 86.09, 72.9, 94.1
a. What is the Median?b. What is the Range?c. What is the IQR?
Minimum1st QuartileMedian3rd QuartileMaximum
Mean
Standard Deviation
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]
Calculator Commands: One Variable Statistics
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
Example #1: Listed below are the weights of 10 people (in lbs)
225, 180, 195, 155, 124, 146, 183, 117, 130, 155
Use the graphing calculator to find:
Mean: __________________
Standard Deviation: _____________
Minimum: _________
1st quartile: _________
Median: _________
3rd quartile: _________
Maximum: _________
Find the following statistics based on the data and calculator information:
Mode: ______________ Range: _____________ IQR: _______
Write the numbers in ascending order:
#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
#3: Explain why the means are the same.You can add different numbers and still get the same total to have the same average.
PRACTICE: Find the mean and standard deviation
PRACTICE FIVE-NUMBER SUMMARY:Find the 5 number summary using the calculator.
Maria:8, 9, 6, 7, 9, 8, 8, 6, 9, 9, 8, 7, 8, 7, 9, 9, 7, 7, 8, 9
Min: __________ Q1: __________
Median: __________
Q3: __________
Max: __________
Calculate:
Range: _________
Interquartile Range: ______
Gia:8, 9, 9, 9, 6, 9, 8, 6, 8, 6, 8, 8, 8, 6, 6, 6, 3, 8, 8, 9
Min: __________ Q1: __________
Median: __________
Q3: __________
Max: __________
Calculate:
Range: _________
Interquartile Range: ______