ĐĎॹá>ţ˙ ˆŠţ˙˙˙†‡˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙˙ěĽÁ'` đżegbjbjëČëČ .l‰˘‰˘e˙˙˙˙˙˙¤ŽŽŽŽŽŽŽÂF7F7F7F7,r7üÂ$[ęz8z8z8z8z8z8z8z8CZEZEZEZEZEZEZ$]hv_RiZuŽz8z8z8z8z8iZŽŽz8z8ŢZ090909z8ŽŽz8Žz8CZ09z8CZ0909RĎSôŽŽŻVz8n8 ş€dĘF79ĂTĎVtôZ0$[áTÎČ_9(Č_<ŻVČ_ŽŻV z8z809z8z8z8z8z8iZiZ09z8z8z8$[z8z8z8z8„2F7ÂÂÂF7ÂÂÂŽŽŽŽŽŽ˙˙˙˙ STATISTICS: Cumulative Frequency NAME: & & & & & & & & & & & & & & & & & & & & & & . The grouped frequency table shows information about the number of hours spent travelling by each of 60 commuters in one week. Number of hours spent travelling (t)Frequency0 < t d" 50 5 < t d" 101410 < t d" 152115 < t d" 201520 < t d" 25725 < t d" 303 Write down the modal class interval. & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & & [1] Work out an estimate for the mean number of hours spent travelling by the commuters that week. …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………… [4] Which class interval contains the median? …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………… [1] Complete the cumulative frequency table. Number of hours spent travelling (t)Cumulative Frequency0 < t d" 5  0 < t d" 10  0 < t d" 15  0 < t d" 20  0 < t d" 25  0 < t d" 30  [1] On the grid below, draw a cumulative frequency graph for the table. [2] (f) Use your graph to find an estimate for the median. …………………………………………………………………………………………………hours. [1] Use your graph to find an estimate for the interquartile range of the number of hours spent travelling by the commuters that week. Show your method clearly. …………………………………………………………………………………………………………………… ………………………………………………………………………………………………………………….. ………………………………………………………………………………………………..hours. [3] Name:…………………………………….. Bob carried out a survey on the number of hours spent on homework a week. He asked 100 students in his school. His results are shown in the table below. Hours (t)Frequency Cumulative Frequency 0 < t d" 2 3t d" 2  2 < t d" 4 7t d" 4  4 < t d" 6 13t d" 6  6 < t d" 8 25t d" 8  8 < t d" 10 32 t d" 10  10 < t d" 12 12 t d" 12  12 < t d" 14 6 t d" 14  14 < t d" 16 2 t d" 16  Complete the cumulative frequency table for the 100 students. Draw the cumulative frequency diagram on the grid below. (c) Use your graph to find the median time spent on homework by these 100 students. ……………………………………………………………………………………………………hours. Use your graph to work out an estimate for the interquartile range. …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… ……………………………………………………………………………………………………hours. (e) Use your graph to estimate how many of these 100 students did more than 9 hours homework in a week. …………………………………………………………………………………………………………………… …………………………………………………………………………………………………………………… ……………………………………………………………………………………………………students. 200 pupils sat an exam. The cumulative frequency curve shows the marks they obtained. Use the graph to find: (a) (i) the median mark. …………………………………………………………………… the lower quartile. ……………………………………..………………………….. the upper quartile. …………………………………………………………………. The interquartile range. ………………………………………………………... (b) If the pass mark was 64 marks, estimate how many pupils passed. …………………………………………………………………………………………………………………… Name:………………………………………………………. The lifespans of 100 domestic cats were recorded. The results are shown in this table. Lifespan (years)<3<6<9<12<15<18<21Cumulative Frequency3823528698100 Illustrate the data by completing the cumulative frequency graph below. Estimate how many cats lived more than ten years. …………………………………………………………………………………………………………………… Use the graph to estimate: the median ………………………………………………………………………………………………………. the interquartile range ………………………………………………………………………………………………………. ………………………………………………………………………………………………………. ………………………………………………………………………………………………………. By the end of these questions you should know: How to construct a cumulative frequency diagram The difference between a cumulative frequency polygon and a cumulative frequency curve. 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The method of constructing a cumulative frequency graph enables you to find the median. The advantage of finding the interquartile range is that it eliminates extreme values and bases the measure of spread on the middle 50% of the data. The cumulative frequency is always the vertical (y) axis. The plotted points can be joined in different ways: By straight lines, to give a cumulative frequency polygon By a freehand curve, to give a cumulative frequency curve. They are both called cumulative frequency diagrams. To plot the top point of each group against the corresponding cumulative frequency How well do you grade yourself? To gain a B, you need to be able to draw a cumulative frequency diagram. 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