Question

The final grades in business mathematics of 60 students at University of Maryland last semester are recorded below. Use the information provided below to answer the questions that follows.
68 54 75 82 68 62 76 73 79 73 60 71 59 75 60
61 65 75 77 66 78 63 78 66 78 75 77 69 74 68
78 61 75 64 79 83 71 79 68 67 78 76 65 71 73
65 73 57 78 62 76 53 74 67 73 75 63 76 75 77
a) Using the interval 50_54, 55_59, 60_64, etc, construct a frequency distribution table showing the class intervals, class boundaries, frequencies, midpoints and cumulative frequencies for each grade.
b) Calculate
i) the approximate mean
ii) variance
iii) the standard deviation.
c) Assume the weights are normally distributed, what is the probability that a particular student selected obtained 78 marks.

Answer 1

Solution

Def and Formulae used

Class Boundaries

Class boundaries are the data values which separate classes. They are not part of the classes or the dataset.

• The lower class boundary of a class is defined as the average of the lower limit of the class in question and the upper limit of the previous class.
• The upper class boundary is defined as average of the upper limit of the class in question and the lower limit of the next class.

Probability (X=x) = No of favourable outcomes / Total outcomes

Please see the attached file.