S.6 Math P2 Revision Qns Caltec S.6

CALTEC ACADEMY MAKERERE A LEVEL APPLIED MATHEMATICS P425/2 REVISION QUESTIONS STATISTICS 1. (a) A sample consists of 15 numbers , 2,4,7,3,5,6,3,6,10,7,8,9,3,4,3. Find: (i) the mean. (ii) standard deviation of the sample. (iii) un biased estimate of population standard deviation (b) The following values were recorded in a frequency table; ∑ 𝑓(𝑥) = 600 , ∑ 𝑓𝑥 2 = 10,000. The standard deviation was calculated as 5. Find the total number of items that were considered. 2. Study the table below; Marks 20 - 24 25 -34 35 - 38 39 - 44 45 - 49 50 - 54 Frequency 6 10 8 9 5 2 (a)(i) Construct a histogram using this data (ii) Use the histogram to estimate the mode. (b). Calculate the mean mark. 3. The table shows the distribution of heights H among spinach plants in a garden Heights (H cm) ≤ 10 ≤ 20 ≤ 30 ≤ 40 ≤ 50 ≤ 60 ≤ 70 ≤ 80 Number of plants 10 16 21 27 14 12 8 2 (a) Calculate; (i) the mean (ii) the median height (iii) standard deviation (b). Plot an ogive for this data and use it to estimate the interval within which the central 80% of the heights lie. (c) Calculate the 10th and 70th percentile range. (d) If a sample of 80 plants is taken randomly from the garden, find the 95% confidence limit for the mean height of the total plants. 4. The Mock examination marks and the Average final examination marks of a certain school are given in the following table Mock Marks 28 34 36 42 52 54 60 Average final examination Marks 54 62 68 70 76 66 74 (a) (i) Plot the marks on the scatter diagram and comment on the relationship between the two marks. (ii) Draw …