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Continuous Numerical Data Learning objectives: represent continuous data interpret histogram with continuous data Homework: Go to mangahigh and practice interpreting histograms/finding the modal class. Ill be monitoring your work.

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Histograms Histograms are different to bar charts. Histograms are frequency diagrams that show grouped data values along the horizontal axis. Histograms can be used to show both discrete and continuous data. Walk Bike Runs 0-9 10-19 Temperature ( o C) 10 14 18 22 26 28 32 Frequency Histograms Grouped Data Runs scored in matches by a batsman last season. Maximum daytime Temperature 20-2930-39 40-49 50-59 Discrete data. Continuous data

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Histograms for Continuous Data A histogram for continuous data is a frequency diagram that shows part of the number line on the horizontal axis. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 …… 5 Frequency Length in cm 4 6 8 10 12 14 10 15 20 Length of Objects Class Interval 4 to 6 This histogram has 5 Class Intervals each of class width 2 Class Interval 10 to 12 Modal Class

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Frequency Time in minutes 102030405060 5 10 15 20 The Histogram below shows the times taken for some students to complete a cross-country race. Histograms for Continuous Data(1) Time Taken for Race Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 1. How many students took more than 30 minutes to complete the race? 16 7 2 25 Histograms for Continuous Data(1) Time Taken for Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 2. How many students took less than 40 minutes to complete the race? 16 9 5 30 Histograms for Continuous Data(1) Time Taken for Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 3. How many students took between 20 and 50 minutes to complete the race? 9 16 7 32 Histograms for Continuous Data(1) Time Taken for Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 4. How many students in total took part in the race? 5 9 16 7 2 39 Histograms for Continuous Data(1) Time Taken for Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 5. The graph clearly shows that some of the students must have taken 35 minutes to complete the race. True or false? Discuss. False Histograms for Continuous Data(1) Time Taken for Race

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Histograms Frequency Time in minutes 102030405060 5 10 15 20 6. One of the students took 60 minutes to complete the race. True or false? Discuss. False Histograms for Continuous Data(1) Time Taken for Race

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Temperature The histogram below shows the maximum daily temperature as recorded over a period of time by a gardener. Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 Histograms for Continuous Data(2) Maximum Daily Temperature

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1. On how many days was the temperature recorded as being less than 18 o C? Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 23 12 35 Histograms for Continuous Data(2) Maximum Daily Temperature

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2. On how many days was the temperature recorded as being greater than 22 o C? Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 7 8 2 17 Histograms for Continuous Data(2) Maximum Daily Temperature

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3. On how many days was the temperature recorded as being between 14 and 26 o C ? Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 23 16 7 46 Histograms for Continuous Data(2) Maximum Daily Temperature

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4. On how many days was the temperature recorded by the gardener? Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 12 23 16 7 8 2 68 Histograms for Continuous Data(2) Maximum Daily Temperature

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5. On most days the temperature was between 14 and 18 o C. True or false? Discuss. Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 Histograms for Continuous Data(2) Maximum Daily Temperature False: The temperature was in that range on only 23 out of 68 days.

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6. The histogram clearly shows that on most days the temperature was between 10 and 18 o C. True or false? Discuss. Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 Histograms for Continuous Data(2) Maximum Daily Temperature True: The temperature was in that range on 35 out of 68 days.

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7. Which of the following statements is true. (a) The minimum temperature was 10 o C. (b) The maximum temperature was 32 o C. Histograms Frequency Temperature ( o C) 101418222628 5 10 15 20 25 32 None of them Histograms for Continuous Data(2) Maximum Daily Temperature

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THE GREEN HOUSE: QUALITY FLORIST Drawing a Histogram Drawing

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Too many! Too few! Between 6 and 9 class intervals looks best. 1. Choose suitable class intervals and display in a frequency table. The following data shows the height (as measured to the nearest cm) of a random selection of cut flowers from Beckys Flower Shop. 42 34 39 49 62 69 28 24 37 38 59 55 47 15 42 68 53 30 45 29 1 0 33 42 61 31 30 21 27 56 50 1 5 35 54 33 45 33 20 44 33 31 FrequencyTally Height (h) in cm Drawing a Histogram from raw data.

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2. Complete the frequency table then draw the histogram. f 5 10 15 0 4 6 8 13 6 3 60 h < 70 50 h < 60 40 h < 50 30 h < 40 20 h < 30 10 h < 20 The following data shows the height (as measured to the nearest cm) of a random selection of cut flowers from Beckys Flower Shop. 42 34 39 49 62 69 28 24 37 38 59 55 47 15 42 68 53 30 45 29 1 0 33 42 61 31 30 21 27 56 50 1 5 35 54 33 45 33 20 44 33 31 FrequencyTally Height (h) in cm Drawing a Histogram from raw data. 1. Choose a suitable class intervals and display in a frequency table. 1020 30 40 50 60 70 Height (cm) Heights of Flowers

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Comparing Histograms Temperature City A 5 10 15 20 25 f 5 10 15 20 25 f The histograms below show the maximum daily temperature as recorded for two European cities over a 60 day period in the summer. One of the cities is 500 miles north of the other. Discuss. 10 Temperature o C 1418222630 34 10 Temperature o C 1418222630 34 Temperature City B Comparing

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The following data shows the height (as measured to the nearest cm) of a random selection of cut flowers from Beckys Flower Shop. 42 34 39 49 62 69 28 24 37 38 59 55 47 15 42 68 53 30 45 29 1 0 33 42 61 31 30 21 27 56 50 1 5 35 54 33 45 33 20 44 33 31 FrequencyTally Height (h) in cm Drawing a Histogram from raw data. Worksheet

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