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. I’ll be monitoring your work.

Histograms Histograms Grouped Data 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 scored in matches by a batsman last season. Histograms Maximum daytime Temperature Grouped Data Frequency Frequency 0-9 10-19 20-29 30-39 40-49 50-59 10 14 18 22 26 28 32 Runs Temperature (oC) Discrete data. Continuous data

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 …… Length of Objects 20 This histogram has 5 Class Intervals each of class width 2 Modal Class 15 Class Interval 4 to 6 Frequency Class Interval 10 to 12 10 5 4 6 8 10 12 14 Length in cm

Histograms for Continuous Data(1) The Histogram below shows the times taken for some students to complete a cross-country race. Time Taken for Race 20 15 Frequency 10 5 Race 10 20 30 40 50 60 Time in minutes

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 1. How many students took more than 30 minutes to complete the race? Time Taken for Race 25 16 7 2

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 2. How many students took less than 40 minutes to complete the race? Time Taken for Race 30 16 9 5

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 3. How many students took between 20 and 50 minutes to complete the race? Time Taken for Race 32 16 9 7

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 4. How many students in total took part in the race? Time Taken for Race 39 16 9 7 5 2

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 5. The graph clearly shows that some of the students must have taken 35 minutes to complete the race. True or false? Discuss. Time Taken for Race False

Histograms for Continuous Data(1) Frequency Time in minutes 10 20 30 40 50 60 5 15 Histograms for Continuous Data(1) 6. One of the students took 60 minutes to complete the race. True or false? Discuss. Time Taken for Race False

Histograms for Continuous Data(2) The histogram below shows the maximum daily temperature as recorded over a period of time by a gardener. 25 Maximum Daily Temperature 20 15 Frequency 10 5 Temperature 10 14 18 22 26 28 32 Temperature (oC)

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 1. On how many days was the temperature recorded as being less than 18 oC? Maximum Daily Temperature 35 23 12

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 2. On how many days was the temperature recorded as being greater than 22 oC? Maximum Daily Temperature 17 8 7 2

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 3. On how many days was the temperature recorded as being between 14 and 26 oC ? Maximum Daily Temperature 46 23 16 7

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 4. On how many days was the temperature recorded by the gardener? 23 Maximum Daily Temperature 68 16 12 8 7 2

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 5. On most days the temperature was between 14 and 18oC. True or false? Discuss. Maximum Daily Temperature False: The temperature was in that range on only 23 out of 68 days.

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 6. The histogram clearly shows that on most days the temperature was between 10 and 18oC. True or false? Discuss. Maximum Daily Temperature True: The temperature was in that range on 35 out of 68 days.

Histograms for Continuous Data(2) Frequency Temperature (oC) 10 14 18 22 26 28 5 15 20 25 32 Histograms for Continuous Data(2) 7. Which of the following statements is true. (a) The minimum temperature was 10oC. (b) The maximum temperature was 32oC. Maximum Daily Temperature None of them

THE GREEN HOUSE: QUALITY FLORIST Drawing a Histogram Drawing

Drawing a Histogram from raw data. The following data shows the height (as measured to the nearest cm) of a random selection of cut flowers from Becky’s Flower Shop. 42 34 39 49 62 69 28 24 37 38 59 55 47 15 42 68 53 30 45 29 10 33 42 61 31 30 21 27 56 50 15 35 54 33 45 33 20 44 33 31 1. Choose suitable class intervals and display in a frequency table. Too many! Frequency Tally Height (h) in cm Too few! Between 6 and 9 class intervals looks best.

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

Comparing Comparing Histograms 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. 25 25 Temperature City A Temperature City B 20 20 15 15 f f 10 10 5 5 10 14 18 22 26 30 34 10 Temperature oC 14 18 22 26 30 34 Temperature oC Comparing

Drawing a Histogram from raw data. The following data shows the height (as measured to the nearest cm) of a random selection of cut flowers from Becky’s Flower Shop. 42 34 39 49 62 69 28 24 37 38 59 55 47 15 42 68 53 30 45 29 10 33 42 61 31 30 21 27 56 50 15 35 54 33 45 33 20 44 33 31 Frequency Tally Height (h) in cm Drawing a Histogram from raw data. Worksheet