STK110 Preparation sheet: TUT 3 2023
Question 1 is based on the following information:
Suppose we are interested in investigating the difference between weeknight hours slept for two
generations. A random sample of 40 Y-ers (Generation Y’ers (Millennials): Born: 1980 – 1995) and 20 Z-
ers (Generation Z’ers: Born: 1996 →) were asked the number of hours they sleep on a randomly chosen
weeknight (minutes were converted to a fraction of an hour). The results are summarised in the following
back-to-back stem-and-leaf diagram:
Weeknight hours slept
Leaf unit = 0.1
Generation Y Generation Z
9 8 8 6 6 5 6
9 8 8 8 8 8 6 6 6 5 5 5 6 6 7
9 8 8 6 3 3 2 2 2 0 0 0 7 0 0 4 6 8 8 9
9 9 9 8 8 6 6 6 5 0 0 8 0 0 5 7 7 7 8 8 8
9 2
a) What is the modal number (mode) of hours slept on a typical weeknight for Generation Y?
b) Determine the 60th percentile of hours slept on a typical weeknight for Generation Y.
c) Using STAT-mode on your calculator, calculate the average and standard deviation hours slept on a
typical weeknight for Generation Z (2 decimals).
d) Determine the coefficient of variation for Generation Z (2 decimals).
e) Based on your answer from Question d and given that 𝑐𝑣𝑦 =13.52% (coefficient variation for
Generation Y), which generation has the lowest relative variability?
1
Question 1 is based on the following information:
Suppose we are interested in investigating the difference between weeknight hours slept for two
generations. A random sample of 40 Y-ers (Generation Y’ers (Millennials): Born: 1980 – 1995) and 20 Z-
ers (Generation Z’ers: Born: 1996 →) were asked the number of hours they sleep on a randomly chosen
weeknight (minutes were converted to a fraction of an hour). The results are summarised in the following
back-to-back stem-and-leaf diagram:
Weeknight hours slept
Leaf unit = 0.1
Generation Y Generation Z
9 8 8 6 6 5 6
9 8 8 8 8 8 6 6 6 5 5 5 6 6 7
9 8 8 6 3 3 2 2 2 0 0 0 7 0 0 4 6 8 8 9
9 9 9 8 8 6 6 6 5 0 0 8 0 0 5 7 7 7 8 8 8
9 2
a) What is the modal number (mode) of hours slept on a typical weeknight for Generation Y?
b) Determine the 60th percentile of hours slept on a typical weeknight for Generation Y.
c) Using STAT-mode on your calculator, calculate the average and standard deviation hours slept on a
typical weeknight for Generation Z (2 decimals).
d) Determine the coefficient of variation for Generation Z (2 decimals).
e) Based on your answer from Question d and given that 𝑐𝑣𝑦 =13.52% (coefficient variation for
Generation Y), which generation has the lowest relative variability?
1
