The following data shows how many employees showed up to work every day for two
weeks
12 18 09 16 11 10 08
10 13 11 15 17 16 11
i. Calculate the interquartile range
ii. Calculate the mean
iii. Calculate the sample standard deviation
b) The following table shows the time students from a college took to complete a marathon.
Time (minutes) 30-32 33-37 38-44 45-47
Frequency 9 a 14 3
Frequency Density 3 4 b 1
i) Find the value of a and b.
ii) Calculate the mean time
iii) Calculate the mode
iv) Calculate the variance
Question Four
a) In a private school students can choose only of French, Spanish or Music as their
Elective. In a group of students, the number of males and females studying Spanish,
French or Music are given in a table below
Spanish French Music
Males 23 12 26
Females 12 15 09
Time (minutes) 30-32 33-37 38-44 45-47
Frequency 9 a 14 3
Frequency Density 3 4 b 1
Course Name and Code – Course Information. Academic Year 2021/2022, Semester II
Page 22 of 36
i) Find the probability that a randomly chosen student
a) studies music [2]
b) studies music or is female [3]
c) is male, given that they do not study Spanish [3]
ii) Determine whether the events ‘a randomly chosen student is a male’ and ‘a randomly
chosen student is studying Music’ are independent, justifying your answer. [3]
iii) Two students are randomly selected, without replacement, what is the probability that
the first student studies Spanish and the second student studies French.