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Histograms & Stemplots for Quantitative Data

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.

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Histograms & Stemplots for Quantitative Data

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  1. Histograms & Stemplotsfor Quantitative Data

  2. 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!

  3. Dotplot for Univariate Quantitative Data Center: about -50 Unusual features: gap at -45 Spread: 48 degrees (-69 to -21) Shape: trimodal

  4. 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

  5. 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

  6. 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

  7. Split Stemplot • 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 70-74 would go in the first 7 stem and 75-79 would go in the second 7 stem Joey’s scores: 7 4 7 5 6 8 8 0 2 4 8 6 7 9 0 1 3 9 6 8 Key: 7 | 4 is score of 74

  8. Back-to-back Stemplot 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

  9. Compare Ruth & Maris • When comparing, use comparative language (higher, better, larger, more, etc) • 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

  10. Histogram of Discrete Data – possible values in center of bar

  11. Histogram of Continuous Data – possible values in between numbers at edges of bar 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

  12. Ch. 3 Test Results 2014 Centered at about 83 Gap between 50-55 Slightly Skewed left, but fairly symmetric Spread/range of about 55

  13. 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 : 689 7 : 2234 7 : 56677899 8 : 0002233334 8 : 5556688889999 9 : 0001234 9 : 5677 10 : 00

  14. 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 so the height represents the count of frequency of each class • All bars should touch, gaps indicate a gap in the data • Ideally there should be about 5- 10 bars

  15. 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 • The histogram and previous stemplot should look the same, just rotated and without individual numbers

  16. Histograms on the calculator • Choose Stat, Edit and enter data into a List • Choose histogram option in StatPlot • Choose the list you used for Xlist, and 1 for Freq if all data is in one list • 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 Graph to see the graph with your fixed window • Press Trace to see details of the graph

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