Histograms & Stemplots for Quantitative Data

Histograms & Stemplotsfor Quantitative Data

Describing Data using Summary Features of Quantitative Variables Center—Location in middle of all data Unusual features - Outliers, gaps, clusters Spread—Measure of variability, range Shape—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 Key Ages of Death of U.S. First Ladies 3 | 4, 6 4 | 3 5 | 2, 4, 5, 7, 8 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 Center: 65 years, Spread: 63 years; Shape: skewed left (towards lower numbers) 3 | 4 indicates 34 years old Stem Leaf—a single digit

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 4 5 6 8 8 0 2 4 6 7 Key: 7 | 4 is score of 74 9 0 1 3 6 8 Center: 86; Spread: 24; Shape: Uniform

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 Stem is split for every 2 leaves— (0, 1), (2, 3), (4, 5), (6, 7), and (8, 9) 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 When comparing data, use comparative language! (higher, more than, etc.) Babe Ruth Roger Maris | 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 Frequency Count This bin represents the # of people whose age is at least 20 but less than 25 Centered at about 35 Skewed right Spread of 90 years Variable being counted

Uniform Distribution from rolling a fair six-sided die 300 times

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 : 44 : 95 : 135 : 5896 : 011114446 : 56666787 : 000122222333447 : 56666788888899999998 : 001122233333344448 : 566666688899999999 : 0122222223344449 : 55566778910 : 0

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

Histograms & Stemplots for Quantitative Data