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

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)

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

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

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

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:

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.

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