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Quantitative Data Continued Histograms

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Used with numerical data Bars touch on histograms Two types – Discrete Bars are centered over discrete values – Continuous Bars cover a class (interval) of values For comparative histograms – use two separate graphs with the same scale on the horizontal axis Would a histogram be a good graph for the fastest speed driven by AP Stat students? Why or why not? Would a histogram be a good graph for the number of pieces of gun chewed per day by AP Stat students? Why or why not?

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Cumulative Relative Frequency Plot (Ogive)... is used to answer questions about percentiles. Percentiles are the percent of individuals that are at or below a certain value. Quartiles are located every 25% of the data. The first quartile (Q1) is the 25th percentile, while the third quartile (Q3) is the 75th percentile. What is the special name for Q2? Interquartile Range (IQR) is the range of the middle half (50%) of the data. IQR = Q3 – Q1

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Histograms Histogram is used when quantitative variables are too many for a stemplot or dotplot. Divide the range of the data into groups of equal width Count the number of individuals in each group Draw the histogram, title, label axis There is no horizontal space between bars unless a group is empty

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Calculator Instructions Calculator STAT choose 1 Edit – Type values into L1 Set Up Histogram – 2 nd Y (Stat Plot) Enter 1 Plot 1 ON Type “histogram” X List: L1 Freq: 1 Quick Graph ZOOM Choose 9 Trace to look at class intervals Set Window to match intervals Graph - Trace

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Histograms The following are ages in months of 15 AP Stat students 195 204 192 193 209 194 199 204 192 214 222 209

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Histogram (Xmin at 189)

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Things to look for Center Shape Spread Outliers Cautions: Pancake and skyscraper effect

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Histogram Example ClassCount 25 to < 34 34 to < 43 43 to < 52 52 to < 61 61 to < 70 70 to < 79 Complete the frequency table below and construct the corresponding histogram. Describe the shape: roughly symmetric, roughly skewed left, roughly skewed right, or no discernible shape. Describe the spread of the distribution. ………………………… What is the center of the distribution? (Hint: look at the original data set) …………… Do there appear to be any obvious outliers? If so, name them. ………………………………… What is the width of each class in the histogram? ………… Could this data set be represented by a pie graph? Why or why not?

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Histogram Example 2 States differ widely with respect to the percentage of college students who are enrolled in public institutions. The U.S. Department of Education provided the accompanying data on this percentage for the 50 U.S. states for fall 1999. Create a histogram to display this data and then give a brief description of the distribution. (use a minimum of 40, and maximum of 100 with class widths of 10) Percentage of College Students Enrolled in Public Institutions 9581858072 7374959189 6391868979 9290938489 9665857692 7569738281 7775705556 8788828184 7680566043 52628082

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