W ARM -U P

D OT P LOTS

D EFINITION A data display in which each data item is shown as a dot above a number line In a dot plot a cluster shows where a group of data points fall. A gap is an interval where there are no data items.

H OW TO M AKE A D OT P LOT V IDEO Creating a Dotplot

S TEPS TO C REATE A D OT P LOT 1. Order numbers from least to greatest. 2. Draw a number line. 3. Label the number line with the minimum and the maximum then all the numbers that fall between them. 4. Put a dot above each number on the number line for each data entry in your set. 5. Don’t forget a title and labels!

6 M AKING A D OT P LOT 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?”

7 M AKING A D OT P LOT FROM L IVE D ATA

8 D OT P LOT E XAMPLE Number of Pets Per Household for Ms. Watts’ Intro Stat Class 2014

9 M AKING A D OT P LOT FROM L IVE D ATA Relative Frequency

10 D OT P LOT : S TATISTICAL V OCABULARY B ACKGROUND 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 Units are important

11 D OT P LOT : S TATISTICAL V OCABULARY B ACKGROUND One Measure of Center- Median 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.

12 D OT P LOT : H OW TO D ESCRIBE I T 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

13 % OF P OPULATION O VER 65

14 P OPULATION OVER 65 D ATA S ORTED BY %

15 Make Dot Plot of State Population Data

16 D OT P LOT : H OW TO D ESCRIBE I T 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.

17 D OT P LOT : W HAT IT L OOKS L IKE Shape: Symmetry Symmetric

18 D OT P LOT : W HAT IT L OOKS L IKE More on Shape: Non Symmetric Skewed Left (negatively skewed) Skewed Right (positively skewed) tail

19 TI83 AND S ORT A SCENDING How to Sort Data in Ascending Order Enter all values in a list at STAT EDIT Exit to Home Screen using 2 nd MODE Hit STAT key. Go to #2 SORT A(. Hit ENTER Type 2 nd 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.

20 G OALS BY US W OMEN ’ S S OCCER

21 G OALS BY US W OMEN ’ S S OCCER O RDERED A SCENDING

22 D OT P LOT OF G OALS BY US W OMEN ’ S S OCCER

23 L IVING IN P OVERTY E AST OF THE M ISSISSIPPI

24 L IVING IN P OVERTY E AST OF THE M ISSISSIPPI O RDERED A SCENDING

25 L IVING IN P OVERTY E AST OF THE M ISSISSIPPI

26 D OT P LOT : M EAN & M EDIAN E SSENTIALS 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. mean median tail

27 D OT P LOT : M EAN & M EDIAN E SSENTIALS 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 tail

28 D OT P LOT : D ESCRIBING P EAKS Peaks Unimodal Bimodal Multimodal (3 or more peaks)

29 D OT P LOT : TI E SSENTIALS Finding Mean and Median Enter your data as a list in STAT EDIT Exit to home screen 2 nd Mode Go to 2 nd STAT. Right Arrow to MATH #3 is Mean; hit Enter; type 2 nd and list #; Enter #4 is Median; hit Enter; type 2 nd and list #; Enter Calculator does not give Mode. You need your eyes for that

30 D OT P LOT : H OW TO D ESCRIBE I T 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.

31 F UEL C ONSUMPTION —D ATA

32 F UEL C ONSUMPTION —D OT P LOT

Y OU TRY IT ! A. In an airline training program, the students are given a test in which they are given a set of tasks and the time it takes them to complete the tasks is measured. The following is a list of the time (in seconds) for a group of new trainees. 61, 61, 64, 67, 70, 71, 71, 71, 72, 73, 74, 74, 75, 77, 79, 80, 81, 81, 83 Display the data in a dot plot.

A NSWER ! Airline Training Program Test New Trainees = 1 person Time in Seconds

A RE THERE ANY CLUSTERS ? Airline Training Program Test New Trainees = 1 person Time in Seconds Yes!

A RE THERE ANY GAPS ? Airline Training Program Test New Trainees = 1 person Time in Seconds Yes!

W HAT IS THE AVERAGE TIME ? Airline Training Program Test New Trainees = 1 person Time in Seconds About 73 seconds

W HAT IS THE MEDIAN TIME ? Airline Training Program Test New Trainees = 1 person Time in Seconds seconds

W HAT IS THE M ODE ? Airline Training Program Test New Trainees = 1 person Time in Seconds seconds

W HAT IS THE R ANGE ? Airline Training Program Test New Trainees = 1 person Time in Seconds seconds

W HAT DOES THE MEDIAN REPRESENT ? Airline Training Program Test New Trainees = 1 person Time in Seconds The center of the data set.

W HAT DOES THE RANGE REPRESENT ? Airline Training Program Test New Trainees = 1 person Time in Seconds The variation in the data set.

T RY AGAIN ! B. In a science class, the students weighed some samples of dirt to the nearest 1/8 pound. The weights of the samples are given below. 1/8 lb, 3/8 lb, ¾ lb, ¼ lb, 1/8 lb, ¼ lb, 7/8 lb, ¼ lb, 3/8 lb, ¼ lb, ½ lb, 3/8 lb Make a dot plot for the data.

A NSWER ! Sample Weights = 1 sample Weight in pounds

A RE THERE ANY CLUSTERS ? Sample Weights = 1 sample Weight in pounds Yes!

A RE THERE ANY G APS ? Sample Weights = 1 sample Weight in pounds Yes!

W HAT IS THE AVERAGE WEIGHT ? Sample Weights = 1 sample Weight in pounds /8 or lb

W HAT IS THE MEDIAN ? Sample Weights = 1 sample Weight in pounds /16 or lb

W HAT IS THE M ODE ? Sample Weights = 1 sample Weight in pounds /8 or 1/4 lb

W HAT IS THE RANGE ? Sample Weights = 1 sample Weight in pounds /8 or 0.75 lb

W HAT DOES THE AVERAGE REPRESENT ? Sample Weights = 1 sample Weight in pounds The center of the data set.

W HAT DOES THE RANGE REPRESENT ? Sample Weights = 1 sample Weight in pounds The variation in the data set.

H OMEWORK