1. Lesson Objective Understand what Cumulative Frequency curves are for Be able to plot a Cumulative Frequency Curve and use it to find the, median, inter-quartile range

2. Weight of the Egg, w (grams)Frequency 30 ≤ w < 4015 40 ≤ w < 5025 50 ≤ w < 6050 60 ≤ w < 7040 70 ≤ w < 8010 Eg A farmer produces eggs for sale. On a Monday he harvests the eggs. He weighs them and puts the results into the table below a)How a many eggs did the farmer harvest on this particular day? b)Estimate the Median weight of the eggs collected. c)Estimate the Inter-quartile Range in the Egg collected.

3. Weight of the Egg, w (grams)Frequency 30 ≤ w < 4015 40 ≤ w < 5025 50 ≤ w < 6050 60 ≤ w < 7040 70 ≤ w < 8010 Eg A farmer produces eggs for sale. On a Monday he harvests the eggs. He weighs them and puts the results into the table below a)How a many eggs did the farmer harvest on this particular day? b)Estimate the Median weight of the eggs collected. c)Estimate the Inter-quartile Range in the Egg collected. A Cumulative Frequency graph helps us to answer these questions more precisely when we have grouped data

4. Weight of the Egg, w (grams) Frequ ency 30 ≤ w < 4015 40 ≤ w < 5025 50 ≤ w < 6050 60 ≤ w < 7040 70 ≤ w < 8010 Weight of the Egg, w (grams) Cum. Freq. 0 ≤ w < 40 0 ≤ w < 50 0 ≤ w < 60 0 ≤ w < 70 0 ≤ w < 80 Cumulative frequency Weight 30354045505560 10 20 30 40 50 60 70 80 90 100 0 110 120 130 140 65707580 A Cumulative Frequency Graph tells you how many eggs were below a particular weight

5. Weight of the Egg, w (grams) Frequ ency 30 ≤ w < 4015 40 ≤ w < 5025 50 ≤ w < 6050 60 ≤ w < 7040 70 ≤ w < 8010 Cumulative frequency Weight 30354045505560 10 20 30 40 50 60 70 80 90 100 0 110 120 130 140 65707580 a)How a many eggs did the farmer harvest on this particular day? b)Estimate the Median weight of the eggs collected. c)Estimate the Inter-quartile Range in the Egg collected. Weight of the Egg, w (grams) Cum. Freq. 0 ≤ w < 40 0 ≤ w < 50 0 ≤ w < 60 0 ≤ w < 70 0 ≤ w < 80

6. a)What is the modal group? b)Complete the cumulative frequency column in the table c) Draw a cumulative frequency curve for your data and use it to estimate: i)The median score in the test ii)The inter-quartile range of the scores iii)The pass mark if only 20 students passed the test

7. a)What is the modal group? b)Complete the cumulative frequency column in the table c) Draw a cumulative frequency curve for your data and use it to estimate: i)The median score in the test ii)The inter-quartile range of the scores iii)The pass mark if only 20 students passed the test ANSWERS. 1. a) 60 – 70 b) 6, 17, 27, 39, 44, 47, 50 d) Median: 58, L.Q. 46, U.Q. 69, I.Q.R. 23 e) 63.

8. A Cumulative Frequency Curve is used for: 1)Estimating the median, and inter-quartile ranges for grouped data 2)For estimating how many items are below or above a particular value

9. Time in mins Cumulative frequency 30354045505560 10 20 30 40 50 60 70 80 90 100 0 Cumulative Frequency goes up the side Horizontal axis has a continuous scale You plot Cumulative Frequency at the end of the interval. (30,10) (30,21) etc A Cumulative frequency graph tells you how many items are below each value. Here 80 people waited for less than 53 mins Waiting TimeCum. Freq. 0 ≤ w < 3510 0 ≤ w < 4021 0 ≤ w < 4546 0 ≤ w < 5073 ……etc.…etc There were 100 people. The median waiting time is that obtained by the 50 th person (half of 100) = 46 mins. To find the Upper quartile, read the time at 75. For the lower quartile read the time at 25. Graph shows how long people waited to be seen at an eye clinic. Key Points: