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Published byKristopher Gardner Modified over 8 years ago

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Histograms, Frequency Polygons, and Ogives (Cumulative Frequency Polygons) OBJ: Make a histogram, frequency polygon and ogive

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P.644 #6 The maximum Fahrenheit temperatures at the municipal airport for each of the 30 days of September were: 827578838174807473625764687076 676360555862595553 5661555260

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ClassRelative Frequency 52 – 556 56 – 594 60 – 636 64 – 672 68 – 712 72 – 754 76 – 792 80 – 834

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Using the frequency table, we can construct the frequency polygon shown at the right below. Its vertical axis can be labeled as integer frequencies. The horizontal axis of the graph shows the middle score for each class. Note that a frequency polygon is usually drawn so that it begins and ends on the horizontal axis. Frequency Polygon F r e q u e n c y Temperatures Class Mark 49.5 Relative Frequency 53.56 57.54 61.56 65.52 69.52 73.54 77.52 81.54

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Using a relative frequency table, we can also construct the cumulative frequency polygon (ogive) shown below. Although its vertical axis can be labeled either in integers or percents, the use of percents is most common. The horizontal axis show the largest score for each class. Ogive R C F e u r l m e a u q t l u i a e v t n e i c v y e Temperatures ClassCumulative Frequency < 520 0 % < 566 20 % < 6010 33 % < 6416 53 % < 6818 60 % < 7220 67 % < 7624 80 % < 8026 87 % < 8430 100 %

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The temperature data can also be organized and displayed in a histogram with either horizontal or vertical bars, as shown below. Notice that the histogram with horizontal bars looks very much like the stem-and leaf plots created earlier. Also notice that a frequency axis isn’t necessary when the frequency is noted on or near each bar. Stem-and-leaf Plot 52335556789 6001223478 70344568 80123 5|2 means 52º ClassRelative Frequency 52 – 556 56 – 594 60 – 636 64 – 672 68 – 712 72 – 754 76 – 792 80 – 834

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The temperature data can also be organized and displayed in a histogram with either horizontal or vertical bars, as shown below. Notice that the histogram with horizontal bars looks very much like the stem-and leaf plots created earlier. Also notice that a frequency axis isn’t necessary when the frequency is noted on or near each bar. F r e q u e n c y Temperatures ClassRelative Frequency 52 – 556 56 – 594 60 – 636 64 – 672 68 – 712 72 – 754 76 – 792 80 – 834

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The temperature data can also be organized and displayed in a histogram with either horizontal or vertical bars, as shown below. Notice that the histogram with horizontal bars looks very much like the stem-and leaf plots created earlier. Also notice that a frequency axis isn’t necessary when the frequency is noted on or near each bar. T e m p a t u r e s Frequency ClassRelative Frequency 52 – 556 56 – 594 60 – 636 64 – 672 68 – 712 72 – 754 76 – 792 80 – 834

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Histogram F r e q u e n c y Temperatures T e m p a t u r e s Frequency

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