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: ______