Answer To Statistic Question

University:
Stanford University
Course:
Introduction to Mathematical Thinking
Academic year:

2023
Views:

214

Pages:

3
Author:

MAlphen

The cumulative frequency graph shows the distribution of marks of 150 students in a Mathematics examination. (a) Use the graph to estimate (i) The number of students who score more than 36 marks, (ii) The interquartile range. (b) Two students are selected at random. Find the probability that (i) Both students score more than 36 marks, (ii) One student scores at most 64 marks while the other student scores morethan 80 marks. (c) Copy and complete the grouped frequency table of the marks of the 150students. (i) 𝑥 (marks) 0<𝑥≤ 20 20 < 𝑥 ≤ 40 40 < 𝑥 ≤ 60 60 < 𝑥 ≤ 80 80 < 𝑥 ≤ 100 No. of studen ts (ii) (d) Using your grouped frequency table, calculate an estimate of (a) The mean mark, (b) The standard deviation. The same group of students took a Science examination. The box and whisker plot shows the distribution of their marks. (i) (ii) Which examination was more difficult? Justify your answer. Compare and comment on the consistency of the performances of the studentsin the two examinations. (e) Another set of 150 students have a higher median but a smaller standard for a Science Examination. Describe how the cumulative frequency curve will be differentfrom the given curve. (f) It was discovered that the marks have been incorrectly measured. The actual mark is5 marks more than what was recorded. Explain how the median and interquartile range of the recorded marks are affected by this error. Ans: (a) (i) 126 students (ii) 73 – 45 = 28 marks (ii) (c) (i) 82 × 20 ×2= 328 x 0 < 𝑥 ≤ 20 20 < 𝑥 ≤ 40 40 < 𝑥 ≤ 60 60 < 𝑥 ≤ 80 80 < 𝑥 ≤ 100 (marks ) (a) 58 marks (ii) No 10 20 40 60 20 (ii)of(b) 21.7 marks studen (d) (i) Science examination is more difficult as it has a lower median mark. ts (ii) The interquartile range for the Science examination is larger. Hence the performance for Science examination is less consistent. (e) (f) Cumulative frequency will shift to the right side and it will be gentler as compared to the cumulative frequency of the Math Exam Median will increase by 5 marks but the Interquartile Range will remain the same.