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We are learning to: - Enhance Mathematical basic skills knowledge. (Which PLT skills?) -Accurately draw cumulative frequency curves and box and whisker plots. (Grade B) Always aim high! LESSON OBJECTIVES Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? AUTHOR Where are we in our journey? Real life cross/curricular links? www.mistrymaths.co.uk

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LEARNING JOURNEY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills

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STARTER Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION TASK 1) 2) 3) 4) Find the n term of: 3, 8, 13, 18,.. 5)6) Find of 1 min 7) Write as a %: 8) Work out: -6 – 9 + 6 9) Work out: 3 x 32 ÷ 4 Write as a percentage. th 2 = 5n - 2 = 8 40 = 1 5 = 2 8 x 5 3 = 10 24 = 5 12 = 6 30 + 5 = 11 30 = 12 21 - 7 = 5 = of 60 seconds 5 12 = 25 seconds = 35 100 = 35% = -9 = 3 x 32 ÷ 16 = 3 x 2 = 6= 6 = 14 20 = 70% = 70 100

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CUMULATIVE FREQUENCY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXAMPLE 1 A golf club has 200 members. Their ages are shown in the frequency table below. Draw a cumulative frequency curve to represent this information. Age (a years)Frequency 0 ≤ a < 108 10 ≤ a < 2026 20 ≤ a < 3032 30 ≤ a < 4045 40 ≤ a < 5037 50 ≤ a < 6029 60 ≤ a < 7016 70 ≤ a < 807 8 +26 +32 +45 +37 +29 +16 +7 Age (a years)Cumulative frequency 8 34 66 111 148 177 193 200 a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < 80

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CUMULATIVE FREQUENCY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXAMPLE 1 A golf club has 200 members. Their ages are shown in the frequency table below. Draw a cumulative frequency curve to represent this information. Age (a years) Cumulative frequency a < 10 a < 20 a < 30 a < 40 a < 50 a < 60 a < 70 a < 80 8 34 66 111 148 177 193 200 10 20 30 40 50 60 70 80 8 34 66 111 148 177 193 200

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CUMULATIVE FREQUENCY EXAMPLE 2 Use your cumulative frequency curve to work out the Median, Lower Quartile, Upper Quartile and Inter-Quartile Range. The draw a whisker plot with this information. We can now use this to find the following information.. Median Lower quartile Upper quartile Lowest Value Highest Value 37 25 51 0 This information can now be used to draw a box and whisker diagram.. 80 Interquartile range 51 - 25 26

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TASK (GRADE B) Every day James does a test to see how many units of sugar are present in his blood. The results of these tests over a period of 50 days are shown in the table below. 1) CUMULATIVE FREQUENCY (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) If the sugar content of James’ blood is greater than 11.5 units, then it is harmful to his health. Use your graph to find an estimate of the number of times these readings were greater than 11.5 units. Show clearly on your graph how you got your answer. 0 2 14 39 47 50 Plot the upper bound (b) MEDIAN = 9 45 (c) 5

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TASK (GRADE B) The lengths of a number of nails were measured to the nearest 0.01 cm, and the following frequency distribution was obtained. 2) CUMULATIVE FREQUENCY (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) Work out the inter-quartile range 2 6 16 40 72 89 96 100 Plot the upper bound (b) MEDIAN = 1.066 LQ = 1.05 UQ = 1.08 IQR = 1.08 – 1.05= 0.03

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TASK (GRADE B) The table shows the times, in minutes, spent on homework one evening by a group of Year 10 students. 3) CUMULATIVE FREQUENCY (a) Complete the table above to find how many students took part in this survey. (b) Draw a cumulative frequency curve to represent the data. (c) Use this curve to find the median time spent on homework by this group of students. (d) Use your curve to find values for the upper quartile and the lower quartile. Hence find the interquartile range. (e) Draw a box and whisker plot for the data. 4 11 21 36 40 102030 40 50 Time (mins) 10 20 30 40 CF MEDIAN = 30mins LQ = 20mins UQ = 37mins IQR = 37 – 20 = 17mins

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TASK (GRADE B) The number of passengers on a bus route was recorded over a period of time, to give the following data. 4) CUMULATIVE FREQUENCY (a) Complete the table and use this to draw a cumulative frequency curve to represent this data. (b) Use your curve to find the median number of passengers on this bus route. (c) Find values for the upper quartile and the lower quartile, and hence find the interquartile range. (d) Draw a box and whisker plot to represent your data. 3 10 22 35 64 90 102030 40 5060 Passengers 10 20 30 40 50 60 70 80 90 CF MEDIAN = 45passengers LQ = 30 UQ = 52 IQR = 52 – 30 = 22passengers

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Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills EXTENSION (GRADE B) 1) Draw cumulative frequency curves and box and whiskers plots for each question below: CUMULATIVE FREQUENCY (a) (b) (c) 8 20 35 55 73 85 95 100 2 5 20 38 63 80 92 100 1 4 1022 25 28 30

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DISCOVERY Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner Which ones are you using?PLT Skills LINK BACK TO OBJECTIVES - Accurately draw cumulative frequency curves and box and whisker plots. What grade are we working at?

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Effective Participator Self Manager Independent Enquirer Creative Thinker Team Worker Reflective Learner PLT Skills Which ones are you using? PLENARY ACTIVITY – GRADE B EXAMINATION QUESTION The cumulative frequency diagram of the heights of 80 red kangaroos is shown below. CUMULATIVE FREQUENCY The table below summarises the heights of 80 grey kangaroos. Explain why the heights of the grey kangaroos are more consistent than the heights of the red kangaroos. You must show your working. (4 marks) Lower Quartile MedianUpper Quartile 85cm105cm120cm Red Kangaroos Grey Kangaroos LQ = 112 UQ = 160 The smaller the IQR the more consistent IQR Grey = 120 – 85 = 35kangaroos IQR Red = 160 – 112 = 48kangaroos As the IQR for grey kangaroos is 13 less, their heights are more consistent.

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Draw your brain What have you learnt? In your brain, write or draw everything you can remember about cumulative frequency curves and box and whisker plots. It can be a skill or a reflection, or something else that might be prominent in your brain. What grade are we working at? Where are we in our journey?

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. How well do you understand the task? I don’t understand I nearly understand I fully understand Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? SELF ASSESSMENT Plenary Activity www.mistrymaths.co.uk

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SELF ASSESSMENT Plenary Activity On your post it notes… Think about how you can improve your work. On your post it notes… Think about how you can improve your work. WWW (What Went Well) EBI (Even Better If) Creative Entrepreneur Responsible Citizen Independent Learner Positive Thinker Team Worker Reflective Learner Enterprise Skills Which ones are you using? www.mistrymaths.co.uk

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TASK (GRADE B) Every day James does a test to see how many units of sugar are present in his blood. The results of these tests over a period of 50 days are shown in the table below. 1) CUMULATIVE FREQUENCY (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) If the sugar content of James’ blood is greater than 11.5 units, then it is harmful to his health. Use your graph to find an estimate of the number of times these readings were greater than 11.5 units. Show clearly on your graph how you got your answer.

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TASK (GRADE B) The lengths of a number of nails were measured to the nearest 0.01 cm, and the following frequency distribution was obtained. 2) CUMULATIVE FREQUENCY (a) Draw a cumulative frequency curve (b) Use your graph to find the median value of x. (c) Work out the inter-quartile range

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