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Includes multiple questions using given graphs, cumulative frequency tables, and histograms to extract the median and quartiles, calculate interquartile range and mean estimates, and determine counts above or within specified thresholds. Also requires constructing cumulative frequency tables and drawing cumulative frequency graphs and accurate histograms from grouped data.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/cumulative-frequency-frequency-density-diagrams-question-paper-7/657402/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/cumulative-frequency-frequency-density-diagrams-question-paper-7/657402.png","ImageObject",300,407,{"name":92,"@type":93},"Kurz","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":24},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"How do you find the median and interquartile range using a cumulative frequency curve?","Question",{"text":112,"@type":113},"Read off the 50th percentile for the median from the cumulative frequency curve, then read the lower and upper quartiles (25th and 75th percentiles). 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Kristina asked 200 people how much water they drink in one day.  \nThe table shows her results.  \n\n| Amount of water (x litres) | Number of people |\n| --- | --- |\n| 0 \u003C x  0.5 | 8 |\n| 0.5 \u003C x  1 | 27 |\n| 1 \u003C x  1.5 | 45 |\n| 1.5 \u003C x  2 | 50 |\n| 2 \u003C x  2.5 | 39 |\n| 2.5 \u003C x  3 | 21 |\n| 3 \u003C x  3.5 | 7 |\n| 3.5 \u003C x  4 | 3 |\n\n(a) Write down the modal interval. [1]  \n(b) Calculate an estimate of the mean. [4]  \n(c) Make a cumulative frequency table for this data. [2]  \n(d) Using a scale of 4 cm to 1 litre of water on the horizontal axis and 1 cm to 10 people on the  \nvertical axis, draw the cumulative frequency graph. [5]  \n(e) Use your cumulative frequency graph to find  \n(i) the median, [1]  \n(ii) the 40th percentile, [1]  \n(iii) the number of people who drink at least 2.6 litres of water. [2]  \n(f) A doctor recommends that a person drinks at least 1.8 litres of water each day.  \nWhat percentage of these 200 people do not drink enough water? [2]  \n3 (a The quiz scores ofa class of n students are shown in the table.  \n\n| Quiz score | 6 | 7 | 8 | 9 |\n| --- | --- | --- | --- | --- |\n| Frequency (number of students) | 9 | 3 | a | 5 |\n\nThe mean score is 7.2. Find  \n(i) a,  \n(ii) n,  \n(iii) the median score.  \n(b) 200 students take a mathematics test.  \nThe cumulative frequency diagram shows the results.  \nCumulative frequency (x marks)  \n200  \n180  \n160  \n140  \n120  \n100  \n80  \n60  \n40  \n20  \n0  \n10 20 30 Mark (x)  \nWrite down  \n(i) the median mark,  \n(ii) the lower quartile,  \n(iii) the upper quartile,  \n(iv) the inter-quartile range,  \n(v) the lowest possible mark scored by the top 40 students,(vi) the number of students scoring more than 25 marks.  \n40  \n50  \n[3]  \n[1]  \n[1]  \n[1]  \n[1]  \n[1]  \n[1]  \n[1]  \n[1]  \n(c) Another group of students takes an English test. The results are shown in the histogram.  \nFrequency density  \n5  \n4  \n3  \n2  \n1  \n0  \n\n| |\n| --- |\n| \u003Cbr>\u003Cbr>10 20 30 40 50 60 70 80 90 100 |\n\nMark (x)  \n100 students score marks in the range 50 \u003C x  75.  \n(i) How many students score marks in the range 0 \u003C x  50? [1]  \n(ii) How many students score marks in the range 75 \u003C x  100?  \n(iii) Calculate an estimate of the mean mark of this group of students. [4]  \n4 The speeds (v kilometres/hour) of 150 cars passing a 50 km/h speed limit sign are recorded. A cumulative frequency curve to show the results is drawn below.  \nCumulative frequency  \n150  \n140  \n130  \n120  \n110  \n100  \n90  \n80  \n70  \n60  \n50  \n40  \n30  \n20  \n10  \n0  \n30 35  \n40 45 50 55 60  \nSpeed (v kilometres / hour)  \n(a) Use the graph to find  \n(i) the median speed, [1]  \n(ii) the inter-quartile range of the speeds, [2]  \n(iii) the number of cars travelling with speeds of more than 50 km/h. [2]  \n(b) A frequency table showing the speeds ofthe cars is  \n(i) Find the value of n. [1]  \n(ii) Calculate an estimate of the mean speed. [4]  \n(c) Answer this part of this question on a sheet of graph paper.  \nAnother frequency table for the same speeds is  \nDraw an accurate h","cbCaiclY4UNboiDF","https://ap.wps.com/l/cbCaiclY4UNboiDF","pdf",568348,"English","# Question 1\n# Question 2\n# Question 3\n# Question 4","[{\"question\":\"How do you find the median and interquartile range using a cumulative frequency curve?\",\"answer\":\"Read off the 50th percentile for the median from the cumulative frequency curve, then read the lower and upper quartiles (25th and 75th percentiles). The interquartile range is the upper quartile minus the lower quartile.\"},{\"question\":\"What does a cumulative frequency table and graph require in this paper?\",\"answer\":\"You must convert the grouped data into cumulative totals across intervals, then plot a cumulative frequency graph using the given axis scales.\"},{\"question\":\"How are frequency density histograms used to estimate totals and the mean?\",\"answer\":\"Use the histogram area (frequency density × class width) to find the number of students in ranges, and calculate an estimated mean from the grouped intervals using the frequency information derived from the histogram.\"}]","Cumulative Frequency & Frequency Density Diagrams - Question Paper 7 | PDF",1792978580,18]