Warm-Up 4/15/2017 In a golf tournament, the top 6 men’s and women’s scores are given. Calculate the mean, median, mode, range, and IQR for each data set.

Unit 4: Describing Data In a golf tournament, the top 6 men’s and women’s scores are given. Compare the spread of the data using the mean and a box and whisker graph.

Box Plot A plot showing the minimum, maximum, first quartile, median, and third quartile of a data set; the middle 50% of the data is indicated by a box. Example:

Box Plot: Pros and Cons Advantages: Shows 5-point summary and outliers Easily compares two or more data sets Handles extremely large data sets easily Disadvantages: Not as visually appealing as other graphs Exact values not retained

Dot Plot A frequency plot that shows the number of times a response occurred in a data set, where each data value is represented by a dot. Example:

Dot Plot: Pros and Cons Advantages: Simple to make Shows each individual data point Disadvantages: Can be time consuming with lots of data points to make Have to count to get exact total. Fractions of units are hard to display.

Histogram A frequency plot that shows the number of times a response or range of responses occurred in a data set. Example:

Histogram: Pros and Cons Advantages: Visually strong Good for determining the shape of the data Disadvantages: Cannot read exact values because data is grouped into categories More difficult to compare two data sets

Measures of Central Tendency (center) Measures of Spread Mean - average Median - middle Mean Absolute Deviation (MAD) Range - difference Interquartile Range (IQR)

Steps to follow when comparing summary statistics. Arrange the data set(s) in order from least to greatest. Calculate: crunch the numbers

Mean: average or x-bar Median: When the data points are organized from least to greatest, the median is the middle number. If there is an even number of data points, the median is the average of the two middle numbers. Mode: Find the number that repeats itself the most. It is possible to have more than one mode Interquartile range: (Q3 – Q1) First, find the Quartiles: Q1 is the first quartile (or 25th percentile). Find the median of the bottom half of numbers. Q3 is the third quartile (or 75th percentile). Find the median of the top half of the numbers. Subtract! Mean Absolute Deviation: on average, how does the data set differ from the mean.

Outlier A data value that is much greater than or much less than the rest of the data in a data set; mathematically, any data less than or greater than is an outlier Example:

Finding the quartiles and inter-quartile range. Example 1: Find the quartiles for the data below. 7, 5, 2, 7, 6, 12, 10, 4, 8, 9 Order the data Lower Quartile = 5 Q1 Median = 7 Q2 Upper Quartile = 9 Q3 2, 4, 5, 6, 7, 7, 8, 9, 10, 12 Inter- Quartile Range = 9 - 5 = 4 Are there any outliers?

Steps to follow when comparing summary statistics. Arrange the data set(s) in order from least to greatest. Calculate: crunch the numbers Graph (box and whisker plot)

To create a box & whisker plot, use a 5 number summary: The minimum value Q1 Median Q3 The maximum value

Interquartile Range: 20 – 6 = 14 Box and Whisker Plot The numbers below represent the number of homeruns hit by players of the McEachern baseball team. 2, 3, 5, 7, 8, 10, 14, 18, 19, 21, 25, 28 Q1 = 6 Q3 = 20 Interquartile Range: 20 – 6 = 14 6 12 20

On the calculator (Graphers only) STAT “1:Edit…” ENTER Clear L1 if necessary, then enter your data Over one to CALC “1:1-Var Stats” ENTER Now you need to tell it to use L1 (2nd 1) ENTER TADA 

Steps to follow when comparing summary statistics. Arrange the data set(s) in order from least to greatest. Calculate: crunch the numbers Graph (box and whisker plot) Comment - Look at the crunched numbers and the graph, in what ways are these data sets similar or different?

= difference Deviation The deviation from the mean is the difference of a data value and the mean of a data set. Mean: 70.5 Mean: 74

Mean Absolute Deviation

Mean Absolute Deviation Find the mean absolute deviation of the data. (Round to the nearest tenth if necessary) 10, 7, 13, 10, 8 87, 75, 85, 77, 74, 82

Several taste tests were conducted around the country on a new hot sauce. Consumers were asked to rate the level of spiciness on a scale of 1 to 10, with 10 being extremely spicy. The mean ratings of these samples were: 2 2 4 4 4 5 5 6 6 6 7 7 7 7 7 7 8 8 9 9 Create a histogram, a dot plot, and a box & whisker plot to represent this data. Compare the data by crunching the numbers.

QUIZ TIME!

Classwork: Homework: Complete the back of the MAD worksheet Worksheet (front and back!)