Histograms & Stemplots for 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

Stemplot for Quantitative Data 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) Stem Leaf—a single digit 3 | 4 indicates 34 years old Key

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) 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 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 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 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: Joey’s first 14 quiz grades in a marking period were: Key: 7 | 4 is score of Center: 86; Spread: 24; Shape: Uniform

Split Stemplot When there are very few stems, do a split stemplot by splitting the stem in half When there are very few stems, do a split stemplot by splitting the stem in half For instance the 7 stem is split so that would go in the first 7 stem and would go in the second 7 stem For instance the 7 stem is split so that would go in the first 7 stem and would go in the second 7 stem Joey’s scores: Key: 7 | 4 is score of 74

Back-to-back Stemplot Babe Ruth Roger Maris Babe Ruth Roger Maris | 0 | 8 | 0 | 8 | 1 | 3, 4, 6 | 1 | 3, 4, 6 5, 2 | 2 | 3, 6, 8 5, 2 | 2 | 3, 6, 8 5, 4 | 3 | 3, 9 5, 4 | 3 | 3, 9 9, 7, 6, 6, 6, 1, 1 | 4 9, 7, 6, 6, 6, 1, 1 | 4 9, 4, 4 | 5 | 9, 4, 4 | 5 | 0 | 6 | 1 0 | 6 | 1 Number of home runs in a season

Compare Ruth & Maris When comparing, use comparative language (higher, better, larger, more, etc) When comparing, use comparative language (higher, better, larger, more, etc) Who’s Better? Who’s Better? Babe Ruth – centered higher at about 47 compared to Maris at 23 Babe Ruth – centered higher at about 47 compared to Maris at 23 Any unusual features? Any unusual features? Maris has a possible outlier at 61 Maris has a possible outlier at 61 Spread? Spread? Maris has larger spread of 53 compared to Babe’s of 38 Maris has larger spread of 53 compared to Babe’s of 38 Shape? Shape? Babe’s is mound shaped and symmetrical, while Maris’s is skewed right with the outlier Babe’s is mound shaped and symmetrical, while Maris’s is skewed right with the outlier

Histogram of Discrete Data – possible values in center of bar

Histogram of Continuous Data – possible values in between numbers at edges of bar Variable being counted 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

Ch. 3 Test Results 2014 Centered at about 83 Gap between Slightly Skewed left, but fairly symmetric Spread/range of about 55

Ch. 3 Test Results 2014 Decimal point is 1 digit(s) to the right of the colon. Leaf unit = 1 4 : 5 5 : 5 : 9 6 : 23 6 : : : : : : : : 00

How to make Histograms Divide the list of data into groups or classes of equal width (0-5, 5-10, 10-15, etc) 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 Scale the horizontal axis using these classes Count the number of individuals in each class Count the number of individuals in each class Scale the vertical axis using the counts Scale the vertical axis using the counts Draw bars so the height represents the count of frequency of each class Draw bars so the height represents the count of frequency of each class All bars should touch, gaps indicate a gap in the data All bars should touch, gaps indicate a gap in the data Ideally there should be about bars Ideally there should be about bars

Make a histogram using Joey’s scores from earlier slide Remember a score on the border between two bars goes in the bar on the right Remember a score on the border between two bars goes in the bar on the right The histogram and previous stemplot should look the same, just rotated and without individual numbers The histogram and previous stemplot should look the same, just rotated and without individual numbers

Histograms on the calculator Choose Stat, Edit and enter data into a List Choose Stat, Edit and enter data into a List Choose histogram option in StatPlot Choose histogram option in StatPlot Choose the list you used for Xlist, and 1 for Freq if all data is in one list Choose the list you used for Xlist, and 1 for Freq if all data is in one list Press Zoom 9 to graph Press Zoom 9 to graph Press Window and round the min, max, and xscl to pretty values. The Xscl will set the width of the bars. Press Window and round the min, max, and xscl to pretty values. The Xscl will set the width of the bars. Press Graph to see the graph with your fixed window Press Graph to see the graph with your fixed window Press Trace to see details of the graph Press Trace to see details of the graph