Bet you’ve never seen a graph like this one before. . . Dot Plots 16 April 2017 16 April 2017 The Dot Plot What is it? How to Draw it Bet you’ve never seen a graph like this one before. . . 10 Dot Plots.ppt 1

What is a Dot Plot? Dot Plots 16 April 2017 16 April 2017 A dot plot is a graph that shows the distribution of a quantitative variable above a number line with small periods, dots, circles or x’s. It plots a quantitative variable against a quantitative variable. Axes on a dot plot A dot plot only has an x-axis. The y-axis is never drawn Advantage of a dot plot Moderate amounts of quantitative data can be quickly visualized Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 2

2 Variables on a dot plot: Dot Plots 16 April 2017 16 April 2017 What is a Dot Plot? 2 Variables on a dot plot: x-axis variable is quantitative and identified y-axis variable is implied since the y-axis is never drawn. y-axis variable is ‘the count’ and so is normally discrete quantitative Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 3

Making a Dot Plot I want to know more about my students who take Intro Stats so I’ve decided to take a survey and make a dot plot of the results I’d like to find out about the pets they have in their household. The question then becomes: “How many pets are in your household?”

Making a Dot Plot from Live Data Dot Plots 16 April 2017 16 April 2017 Making a Dot Plot from Live Data 10 Dot Plots.ppt 5

Dot Plot Example Dot Plots 16 April 2017 16 April 2017 10 Dot Plots.ppt 6

Freq Table Example 4 Classes Combined Dot Plots 16 April 2017 16 April 2017 Freq Table Example 4 Classes Combined Mean = 2.52 pets Median = 2 pets Mode = 0 pets (37x) Range = 30 pets Spread = 0 - 30 pets n = 134 students 10 Dot Plots.ppt 7

Dot Plot Example 4 Classes Combined Dot Plots 16 April 2017 16 April 2017 Dot Plot Example 4 Classes Combined 8 10 Dot Plots.ppt 8

Dot Plot: Statistical Vocabulary Background 16 April 2017 16 April 2017 Spread (also called Variability) The spread of data in statistics is the smallest value in a data set and the largest value It is always expressed as 2 numbers Prefer to write smallest then largest number Units are important Range The range of data in statistics is the difference between the smallest value and the largest value Take the spread and subtract the two numbers: large – small Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 9

Dot Plot: Statistical Vocabulary Background 16 April 2017 16 April 2017 One Measure of Center One measure of the center of a data distribution is the median, the place where the data tends to be ½ above and ½ below. Units are important Mode The mode of data is a place or places with the largest number of data with the same value. Units are important. Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 10

Dot Plot: How to Describe It Dot Plots Dot Plot: How to Describe It 16 April 2017 16 April 2017 Shape The shape of a data distribution possibilities: 1) Symmetry Symmetric Also ‘Fairly Symmetrical’ Skewed Left (negatively skewed) Skewed Right (positively skewed) 2) Peaks Single Peaked (unimodal) Double Peaked (bimodal) Multi Peaked (multimodal) NOTE: Data have modes, dot plots have peaks Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 11

Student Scores in Anderson’s Cr Writing

Student Scores in Anderson’s Cr Writing

% of Population Over 65

Population over 65 Data Sorted by %

Make Dot Plot of State Population Data

Dot Plot: How to Describe It Dot Plots 16 April 2017 16 April 2017 More on Shape Symmetric When the left & right sides of a distribution are mirror images of one another Fairly Symmetric When the left and right sides of a distribution are almost mirror images of one another, but there are small exceptions. Skewed Left (negatively skewed) If a distribution extends much farther out to the left. The direction of skewness is on the side of the longer tail, in this case LEFT. Skewed Right (positively skewed) If a distribution extends much farther out to the right. The direction of skewness is on the side of the longer tail, in this case RIGHT. Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 17

Dot Plot: What it Looks Like Dot Plots 16 April 2017 16 April 2017 Dot Plot: What it Looks Like Shape: Symmetry Symmetric Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 18

Dot Plot: What it Looks Like Dot Plots 16 April 2017 16 April 2017 Dot Plot: What it Looks Like More on Shape: Non Symmetric Skewed Left (negatively skewed) Skewed Right (positively skewed) tail Categorical or Qualitative Quantitative or Numerical tail 10 Dot Plots.ppt 19

Goals by US Women’s Soccer

Goals by US Women’s Soccer Ordered Ascending

Dot Plot of Goals by US Women’s Soccer

Living in Poverty East of the Mississippi

Living in Poverty East of the Mississippi Ordered Ascending

Living in Poverty East of the Mississippi

Dot Plot: Mean & Median Essentials Dot Plots Dot Plot: Mean & Median Essentials 16 April 2017 16 April 2017 Skew on a dot plot in relation to mean and median You’ve drawn the line that connects the dot plot points on the top of the distribution. The line clearly shows right or left skew. If you have right skew, the mean will be to the right of (greater than) the median, as the mean follows the tail of the distribution. median Categorical or Qualitative Quantitative or Numerical mean tail 10 Dot Plots.ppt 26

Dot Plot: Mean & Median Essentials Dot Plots Dot Plot: Mean & Median Essentials 16 April 2017 16 April 2017 Skew on a dot plot in relation to mean and median If you have left skew, the mean will be to the left of (less than) the median, as the mean follows the tail of the distribution. median mean Categorical or Qualitative Quantitative or Numerical tail 10 Dot Plots.ppt 27

Dot Plot: Describing Peaks Dot Plots Dot Plot: Describing Peaks 16 April 2017 16 April 2017 Peaks Unimodal Bimodal Categorical or Qualitative Quantitative or Numerical Multimodal (3 or more peaks) 10 Dot Plots.ppt 28

How to Sort Data in Ascending Order TI83 and Sort Ascending How to Sort Data in Ascending Order Enter all values in a list at STAT EDIT Exit to Home Screen using 2nd MODE Hit STAT key. Go to #2 SORT A(. Hit ENTER Type 2nd 1 (if the data is in List 1). Hit Enter Done appears Check your data in List 1. It should be sorted. Use your eyes to find the range & spread from the sorted list.

Dot Plot: TI Essentials Dot Plots Dot Plot: TI Essentials 16 April 2017 16 April 2017 Finding Mean and Median Enter your data as a list in STAT EDIT Exit to home screen 2nd Mode Go to 2nd STAT. Right Arrow to MATH #3 is Mean; hit Enter; type 2nd and list #; Enter #4 is Median; hit Enter; type 2nd and list #; Enter Calculator does not give Mode. You need your eyes for that Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 30

Glucose Blood Levels Dot Plots 16 April 2017 16 April 2017 Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 31

Glucose Blood Levels Dot Plots 16 April 2017 16 April 2017 Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 32

WBNA EAST Free Throws—Data in Ascending Order

WBNA Free Throws—Dot Plot

Dot Plot: How to Describe It Dot Plots Dot Plot: How to Describe It 16 April 2017 16 April 2017 Unusual Features. Possibilities include-- Potential Outliers: any data value that falls out of the pattern of the rest of the distribution. A potential outlier will lie at either extreme of the data when it is written in order. (We will learn how to calculate actual outliers later. For now, we will call these points potential outliers) Clusters: isolated groups of values. Clusters begin when frequency >1 and end before frequency returns to 1 or zero. Gaps: large spaces between values. Write gap values from beginning empty space to end empty space. A gap of one number is NOT a gap. Categorical or Qualitative Quantitative or Numerical 10 Dot Plots.ppt 35

Fuel Consumption—Data

Fuel Consumption—Dot Plot