1 Statistics Paper1 1.At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100 mathematicians. 2. The mean of the population x1, x2, ........, x25 is m. Given that 251iix= 300 and 2512)–(iimx= 625, find (a) the value of m; (b) the standard deviation of the population. 3.The cumulative frequency curve below shows the marks obtained in an examination by a group of 200 students. 2001901801701601501401301201101009080706050403020100102030405060708090100Mark obtainedNumberofstudents(a) Use the cumulative frequency curve to complete the frequency table below. Mark (x) 0 x< 20 20 x< 40 40 x< 60 60 x< 80 80 x< 100 Number of students 22 20 (b) Forty percent of the students fail. Find the pass mark. 4.The cumulative frequency curve below shows the heights of 120 basketball players in centimetres.
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2 1201101009080706050403020100160165170175180185190195200Height in centimetresNumber of playersUse the curve to estimate (a) the median height; (b) the interquartile range. 5.The four populations A, B, C and D are the same size and have the same range. Frequency histograms for the four populations are given below. ..................
3 6.The cumulative frequency graph below shows the heights of 120 girls in a school. 1301201101009080706050403020100185180175170165160155150Cumulative frequencyHeight in centimetres (a) Using the graph (i) write down the median; (ii) find the interquartile range. (b) Given that 60of the girls are taller than acm, find the value of a. 7.A test marked out of 100 is written by 800 students. The cumulative frequency graph for the marks is given below.