stats.pdf - 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

# stats.pdf - Statistics Paper1 1 At a conference of 100...

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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 x 1 , x 2 , ........ , x 25 is m . Given that 25 1 i i x = 300 and 25 1 2 ) ( i i m x = 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. 200 190 180 170 160 150 140 130 120 110 100 90 80 70 60 50 40 30 20 10 0 10 20 30 40 50 60 70 80 90 100 Mark obtained Number of students (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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2 120 110 100 90 80 70 60 50 40 30 20 10 0 160 165 170 175 180 185 190 195 200 Height in centimetres Number of players Use 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. 130 120 110 100 90 80 70 60 50 40 30 20 10 0 185 180 175 170 165 160 155 150 Cumulative frequency Height in centimetres (a) Using the graph (i) write down the median; (ii) find the interquartile range. (b) Given that 60 of the girls are taller than a cm, 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.

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