Histograms & Stemplots for Quantitative Data

Describing Data using Summary Features of Quantitative Variables C enter — Location in middle of all data U nusual features - Outliers, gaps, clusters S pread—Measure of variability, range S hape—Distribution pattern: symmetric, skewed, uniform, bimodal, etc.

CUSS in context!

Dotplot for Univariate Quantitative Data

Center: about -50 Unusual features: gap at -45 Spread: 48 degrees (-69 to -21) Shape: trimodal, representing 3 seasons

Stemplot for Quantitative Data

Ages of Death of U.S. First Ladies 3 | 4, 6 4 | 3 5 | 2, 4, 5, 7, 8

3 | 4

indicates 34 years old 6 | 0, 0, 1, 2, 4, 4, 4, 5, 6, 9 7 | 0, 1, 3, 4, 6, 7, 8, 8 8 | 1, 1, 2, 3, 3, 6, 7, 8, 9, 9 9 | 7

Stem Leaf

—a

Key

single digit Center: 65 years, Spread: 63 years; Shape: skewed left (towards lower numbers)

How to make a Stemplot (Stem and Leaf Plot)    Separate each observation into a stem (all but the last digit) and a leaf (the last digit)  Sometimes rounding to the nearest hundred, thousand, etc. is a good idea when there are a lot of digits to consider Write the stems in a vertical column in order from smallest to largest and draw a vertical line at the right of the column Write each leaf in the row to the right of its stem in increasing order

 Make a stemplot with the following data Joey’s first 14 quiz grades in a marking period were: 86 84 91 75 78 80 74 87 76 96 82 90 98 93 7 8 9 4 5 6 8 0 2 4 6 7 0 1 3 6 8 Key: 7 | 4 is score of 74 Center: 86; Spread: 24; Shape: Uniform

Stem is split for every 2 leaves— (0, 1), (2, 3), (4, 5), (6, 7), and (8, 9)

Split Stemplot

1 | 7 1 | 8, 9, 9, 9, 9, 9 2 | 0, 0, 0, 0, 1, 1, 1, 1, 1, 1 2 | 2, 2, 2, 3, 3 2 | 4, 5 2 | 2 | 8 3 | 0, 1 Age of 27 students randomly selected from Stat 303 at A&M

Split Stemplot

1 | 1 | 7, 8, 9, 9, 9, 9, 9 2 | 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4 2 | 5, 8 3 | 0, 1 3 | Stem is split for every 5 leaves—(0 thru 4) and (5 thru 9) Age of 27 students randomly selected from Stat 303 at A&M

Back-to-back Stemplot

Babe Ruth Roger Maris

When comparing data, use comparative language! (higher, more than, etc.) | 0 | 8 | 1 | 3, 4, 6 5, 2 | 2 | 3, 6, 8 5, 4 | 3 | 3, 9 9, 7, 6, 6, 6, 1, 1 | 4 9, 4, 4 | 5 | 0 | 6 | 1

Number of home runs in a season

Compare Ruth & Maris

    Who’s Better?

 Babe Ruth – centered higher at about 47 compared to Maris at 23 Any unusual features?

 Maris has a possible outlier at 61 Spread?

 Maris has larger spread of 53 compared to Babe’s of 38 Shape?

 Babe’s is mound shaped and symmetrical, while Maris’s is skewed right with the outlier

Histogram

TX_betw eenHoustonDallas 120

Frequency Count

100 This bin represents the # of people whose age is at least 20 but less than 25 80 Histogram 60 40 Centered at about 35 Skewed right Spread of 90 years 20 0 20 40 Variable being counted age 60 80 100

70 60 50 40 30 20 10 0 Uniform Distribution from rolling a fair six-sided die 300 times 42 54 46 45 59 54 1 2 3 4

Face of Fair Six-sided Die

5 6

How to make Histograms

     Divide the list of data into groups or classes of equal width (0-5, 5-10, 10-15, etc) Scale the horizontal axis using these classes Count the number of individuals in each class Scale the vertical axis using the counts Draw bars representing the count for each class, so each bar has equal width

    

Histograms on the calculator

Enter data into List Choose histogram option in StatPlot Choose the list you used for Xlist Choose 1 for Freq or a 2nd list if data is stored in two lists (values in one, frequency in another) Zoom 9:statplot will scale it for you but check the Window to make sure you have reasonable values of min & max for both x (values) and y (frequency count). The Xscl will set the width of the bars.

Ch. 3 Test Results

Centered at about 80 No unusual features Skewed left Spread of about 60

Ch. 3 Test Results

Decimal point is 1 digit(s) to the right of the colon. 4 : 4 4 : 9 5 : 13 5 : 589 6 : 01111444 6 : 5666678 7 : 00012222233344 7 : 5666678888889999999 8 : 00112223333334444 8 : 56666668889999999 9 : 012222222334444 9 : 555667789 10 : 0

Make a histogram using Babe Ruth’s data from the earlier slide