Standard Deviation and Cumulative Frequency

Statistics-1 1. One thousand candidates sit an examination. The distribution of marks is shown in the followers grouped oftenness give in. Marks1101120213031404150516061707180819091100 Number of candidates155010017026022090453020 (a)Copy and complete the following table, which presents the above data as a cumulative frequency distribution. (3) Mark? 10? 20? 30? 40? 50? 60? 70? 80? 90? 100 Number of candidates1565905 b)Draw a cumulative frequency graph of the distribution, using a scale of 1 cm for 100 candidates on the perpendicular axis and 1 cm for 10 marks on the horizontal axis. (5) (c)Use your graph to answer parts (i)(iii) below, (i)Find an estimate for the median score. (2) (ii)Candidates who scored less than 35 were required to retake the examination. How many candidates had to retake? (3) (iii)The highest-scoring 15% of candidates were awarded a distinction. Find the mark above which a distinction was awarded. (3) Total 16 marks) 2. At a conference of 100 mathematicians there atomic number 18 72 men and 28 women. The men get hold of a cogitate height of 1. 79 m and the women have a mean height of 1. 62 m. Find the mean height of the 100 mathematicians. (Total 4 marks) 3. The mean of the population x1, x2, .. , x25 is m. Given that = 300 and = 625, find (a)the value of m (b)the standard deviation of the population. (Total 4 marks) 4. A supermarket records the amount of money d pass by customers in their store during a busy period.The results are as follows Money in $ (d)02020404060608080100100120120140 Number of customers (n)2416224018104 (a)Find an estimate for the mean amount of money spent by the customers, giving your answer to the nearest dollar ($). (2) (b)Copy and complete the following cumulative frequency table and use it to draw a cumulative frequency graph. Use a scale of 2 cm to represent $20 on the horizontal axis, and 2 cm to represent 20 customers on the vertical axis. (5) Money in $ (d)