Unit 3: Statistics Final Exam Review

Topics to cover Dot Plots Histograms 5 Number Summary Outliers Box and Whisker Plots Stem and Leaf Plots Double Stem and Leaf Plots

Dot Plots A Dot Plot is a statistical chart containing DATA POINTS plotted on a simple scale To make a dot plot, place a DOT on top of the number every time the data point shows up in the set. Example:

Dot Plots You Try! Students from River City High School were randomly selected and asked, “How many pets do you currently own?” The results are recorded below:

Histograms A Histogram is a statistical chart that shows the FREQUENCY of data. To draw a histogram, COUNT how many data points fall into each RANGE and then draw a bar to represent the frequency. Example:

Histograms You Try! The following data represents the number of tweets per week. 61 59 66 69 47 52 16 13 50 63 44 53 49 40

5 Number summary MINIMUM – the LOWEST number in the data set Q1 – The MEDIAN of the LOWER HALF of the data Q2 – The MEDIAN of the data Q3 – The MEDIAN of the UPPER HALF of the data MAXIMUM– the HIGHEST number in the data set

5 Number summary Example: {0, 3, 6, 8, 10, 12, 14} Minimum – 0 Q1 – 3 Maximum – 14 You Try! {8, 13, 15, 21, 23, 33, 44} Minimum – Q1 – Q2 – Q3 – Maximum –

5 Number summary You Try! {5, 12, 7, 4, 3, 10, 1, 4} Minimum – Q1 – If the data is not in order from lowest to highest, you must put the data in ORDER first If 2 numbers are in the middle of the data, to find the median, find the AVERAGE of the 2 numbers. Example: {19, 2, 13, 8, 0, 5, 3, 2} Put data in order: {0, 2, 2, 3, 5, 8, 13, 19} Minimum – 0 Q1 – 2 (Average of 2 and 2) Q2 – 4 (Average of 3 and 5) Q3 – 11 (Average of 8 and 13) Maximum – 19 You Try! {5, 12, 7, 4, 3, 10, 1, 4} Minimum – Q1 – Q2 – Q3 – Maximum –

Outliers Some data sets include numbers that are either TOO SMALL or TOO BIG and don’t fit in with the other numbers in the set. These are called OUTLIERS To find any outliers, follow these steps: 1. Find the 5 NUMBER SUMMARY 2. Find the INTERQUARTILE RANGE (IQR) which is the difference between Q1 and Q3 3. Multiply the IQR by 1.5 to find the “magic number” 4. If any numbers in the data are LOWER THAN Q1 minus the magic number or LARGER THAN Q3 plus the magic number, they are OUTLIERS

Outliers Example: {0, 15, 16, 17, 18, 20, 55} Minimum – 0 Q1 – 15 Q2 – 17 Q3 – 20 Maximum – 55 IQR is 20 – 15, so the IQR is 5. 5 x 1.5 = 7.5 Q1: 15 – 7.5 = 7.5 Q3: 20 + 7.5 = 27.5 0 is less than 7.5 and 55 is more than 27.5, therefore 0 and 55 are outliers.

Outliers You Try! {2, 15, 19, 20, 21, 22, 34} Minimum: Q1: Q2: Q3: Maximum: IQR: _______ Outliers? _________

Box and Whisker Plots Box and Whisker plots are a visual representation of the 5 NUMBER SUMMARY The whiskers are created from the MINIMUM and the MAXIMUM The box is made from Q1, Q2 (the median) and Q3. Example:

Box and Whisker Plots You Try! Make a box and whisker plot of the following data: {60, 60, 62, 63, 63, 66, 66, 66, 67, 68, 69, 69, 69, 69, 70, 70} Minimum: Q1: Q2: Q3: Maximum: 60 61 62 63 64 65 66 67 68 69 70

Stem and Leaf Plots A plot where each data value is split into a “LEAF" (usually the last digit) and a “STEM" (the other digits). If any data points are only single digits, use 0 as the stem. Example: {22, 26, 27, 31, 33, 35, 42, 44, 46, 57, 58, 59, 61, 63, 64, 65, 67} 

Stem and Leaf Plots You Try! Make a stem and leaf plot for the following data: {12, 45, 23, 44, 18, 33, 9, 51, 17, 23, 43, 33, 30, 13, 10, 7, 40}

Double Stem and Leaf Plots Double Stem and Leaf Plots – Allow you to plot 2 different sets of data on one stem and leaf plot. One set of data will be written on the LEFT, and the other set will be written on the RIGHT. The STEMS will be written in the MIDDLE Example:

Double Stem and Leaf Plots Example: The following data represents the ages of 10 Democrats and 10 Republicans in the Senate.

Double Stem and Leaf Plots You Try! Make a double stem and leaf plot for the following data: Males: Females: 9 6 12 11 56 43 38 14 26 13 18 12 22 45 39 10 8 13 21 27 7 11 19 32 20 23 16 Males Stem Females

ALL DONE