Mathematics Higher Level Robert Joinson

©Sumbooks2002Higher Level73. Mean and Standard Deviation1. Nigel weighs 10 bags of potatoes. His readings are:5.01kg, 5.03kg, 5.07kg, 5.05kg, 5.08kg, 5.04kg, 5.03kg, 5.01kg, 5.04kg, 5.08kg.a) Calculate the mean and standard deviation of the readings.b) Nigel notices a sign on the scales saying that all measurements are undersize by 0.02kg.Explain the effect this has on (i) the mean (ii) the standard deviation.2. The heights of the children in year 10 were measured by the school nurse. Her results areshown below.Height of child (cm) Frequency f Mid point x120 < h ≤ 130 3130 < h ≤ 140 7140 < h ≤ 150 20150 < h ≤ 160 54160 < h ≤ 170 32170 < h ≤ 180 9a) Complete the table for the mid point values.b) Use the mid point values to calculate (i) the mean (ii) the standard deviation, for theheights of the children, giving your answer correct to one decimal place.3. The weekly wages of the employees at a supermarket are given in the table below.Wage £ Frequency f Mid Value x80 < £ ≤ 120 5120 < £ ≤ 160 8160 < £ ≤ 200 9200 < £ ≤ 240 11240 < £ ≤ 280 14280 < £ ≤ 320 17320 < £ ≤ 360 3a) Complete the table for the mid values.b) Using the mid point values, calculate the mean and standard deviation of the distribution,giving your answers correct to two decimal places.c) It is decided to give each person in the store a bonus of £10 for one week. What effect willthis have on the mean and the standard deviation for that week?4. The list below shows the ages of the 30 members of a tennis club.21 65 33 29 32 29 53 61 39 4842 45 46 27 48 35 46 25 43 5924 37 44 63 39 22 38 33 55 51a) Complete this grouped frequency table.Age (years) Frequency Mid value20 ≤ a < 30etcb) Use this table of values to calculate an estimate of the mean and standard deviation of thedistribution.c) At the Badminton club, the mean age is 48 and the standard deviation is 8.4. Comment onthe differences between these figures and those for the tennis club.