Chap 1: Exploring Data 1.3: Measures of Center 1.4: Quartiles, Percentiles, and Box Plots 1.7: Variance and Standard Deviation.

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Presentation transcript:

Chap 1: Exploring Data 1.3: Measures of Center 1.4: Quartiles, Percentiles, and Box Plots 1.7: Variance and Standard Deviation

The Presentation of Data Dotplot (Dot-frequency diagram) Stemplot Stem: first digit or digits Leaf: last digit Frequency Table

Summation Notation

Suppose we wanted to sum the first 10 numbers: Let’s build a table:

Summation Notation

Using Summation Notation to Solve a Problem The corner section of a football stadium has 15 seats in the first row and 40 rows in all. Each successive row contains two additional seats. How many seats are in this section?

Using Summation Notation to Solve a Problem

Summation Notation

Mean

Median The middle value of a set of data Order the data from smallest to largest The median is the middle value When there exists an even number of elements, the median is the average of the two middle values Our previous data: 3, 3, 4, 6, 7 Median = 4

Mode The value that appears the most number of times in a set of data Our previous data: 3, 3, 4, 6, 7 Mode = 3

Measures of Center

Percentile The p th percentile of a set of numbers is a value in the set such that p percent of the numbers are less than or equal to that value. Max = 100 th percentile Min = 0 th percentile Median = 50 th percentile

Quartiles

Five Number Summary 1)Minimum 2)1 st Quartile = Lower Quartile 3)2 nd Quartile = Middle Quartile 4)3 rd Quartile = Upper Quartile 5)Maximum

Five Number Summary Calculate the average daily high temperature in Colorado Springs for June 2014 Generate a Five Number Summary for the daily high temperatures in Colorado Springs for June 2014 June 2014 Temperatures

June 2014 Temperatures

Box Plot Box-and-Whisker Plot A visual representation of a five-number summary 1)Draw a number line including the minimum and maximum data values 2)Draw a rectangle with opposite sides at the lower and upper quartiles of the data (hinges) 3)In the box, draw a segment parallel to the hinges at the median 4)Draw segments from the midpoints of the hinges to the min and max values (whiskers)

Box Plot Box-and-Whisker Plot

Outliers and the Interquartile Range

June 2014 Temperatures

Calculating the Variance and Standard Deviation

Variance and Standard Deviation

Example Problem (Test Scores)

Chap 1 Homework 1.3: Page 26#14 – : Pages 34 – 35 # 1 – : Page 58 # 1, 4, 5