continuous numerical data learning objectives: represent continuous data interpret histogram with...
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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. I’ll be monitoring your work.
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
Runs0-9 10-19
Temperature (oC)10 14 18 22 26 28 32
Frequency
Frequency
Histograms
Grouped Data
Runs scored in matches by a batsman last season.
Maximum daytime
Temperature
20-29 30-39 40-49 50-59
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
……
5
Freq
uen
cy
Length in cm4 6 8 10 12 14
10
15
20Length 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
Fr
eq
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
Freq
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
Fr
eq
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
Freq
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
F
req
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
F
req
uen
cy
Time in minutes10 20 30 40 50 60
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
Histograms
F
req
uen
cy
Time in minutes10 20 30 40 50 60
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
Temperature
The histogram below shows the maximum daily temperature as recorded over a period of time by a gardener.
Fre
qu
en
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
Histograms for Continuous Data(2)
Maximum Daily Temperature
1. On how many days was the temperature recorded as being less than 18 oC?
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
23
12
35
Histograms for Continuous Data(2)
Maximum Daily Temperature
2. On how many days was the temperature recorded as being greater than 22 oC?
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
78
2
17
Histograms for Continuous Data(2)
Maximum Daily Temperature
3. On how many days was the temperature recorded as being between 14 and 26 oC ?
Histograms
Freq
uen
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
23
16
7
46
Histograms for Continuous Data(2)
Maximum Daily Temperature
4. On how many days was the temperature recorded by the gardener?
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
12
23
16
7 8
2
68
Histograms for Continuous Data(2)
Maximum Daily Temperature
5. On most days the temperature was between 14 and 18oC. True or false? Discuss.
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
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.
6. The histogram clearly shows that on most days the temperature was between 10 and 18oC. True or false? Discuss.
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
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.
7. Which of the following statements is true. (a) The minimum temperature was 10oC. (b) The maximum temperature was 32oC.
Histograms
F
req
uen
cy
Temperature (oC)10 14 18 22 26 28
5
10
15
20
25
32
None of them
Histograms for Continuous Data(2)
Maximum Daily Temperature
THE GREEN HOUSE: QUALITY
FLORIST
Drawing a HistogramDrawing
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 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
TallyHeight (h)
in cm
Drawing a Histogram from raw data.
2. Complete the frequency table then draw the histogram.
f5
10
15
04
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 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
TallyHeight (h)
in cm
Drawing a Histogram from raw data.
1. Choose a suitable class intervals and display in a frequency table.
10 20 30 40 50 60 70Height (cm)
Heights of Flowers
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.
10Temperature oC
14 18 22 26 30 34 10Temperature oC
14 18 22 26 30 34
Temperature City B
Comparing
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
TallyHeight (h)
in cm
Drawing a Histogram from raw data.
Worksheet