## MATH1005 Quizzes

Quiz 1: Data sets
Question 1 Questions
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the mean of the above data, to 2 decimal places. Exactly one option must be correct)
 a) 2.8 b) 3 c) 2.81 d) 2.8

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the median of the above data. Exactly one option must be correct)
 a) 3 b) 2 c) 2.5 d) 3.5

Choice (a) is correct!
Since $n=32$, the median is the average of the 16th and 17th entries which is 3.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the upper quartile of the above data. Exactly one option must be correct)
 a) 4.5 b) 3.5 c) 4 d) 2

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
Since $n=32$, the upper quartile is the average of the 24th and 25th entries, which is 4.
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the lower quartile of the above data. Exactly one option must be correct)
 a) 2 b) 3 c) 1 d) 1.5

Choice (a) is correct!
Since $n=32$, the lower quartile is the average of the 8th and 9th entries which is 2.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the interquartile range. Exactly one option must be correct)
 a) 3 b) 2 c) 1.5 d) 2.5

Choice (a) is incorrect
Choice (b) is correct!
$IQR\phantom{\rule{1em}{0ex}}=UQ\phantom{\rule{1em}{0ex}}-LQ\phantom{\rule{1em}{0ex}}=4-2=2$.
Choice (c) is incorrect
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the upper threshold for the above data. Exactly one option must be correct)
 a) 6 b) 5 c) 5.5 d) 4.5

Choice (a) is correct!
$UT\phantom{\rule{1em}{0ex}}=UQ\phantom{\rule{1em}{0ex}}+IQR\phantom{\rule{1em}{0ex}}=4+2=6$.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the lower threshold for the above data. Exactly one option must be correct)
 a) 0.5 b) 1 c) 0 d) -1

Choice (a) is incorrect
Choice (b) is incorrect
Choice (c) is correct!
$LT\phantom{\rule{1em}{0ex}}=LQ\phantom{\rule{1em}{0ex}}-IQR\phantom{\rule{1em}{0ex}}=2-2=0$.
Choice (d) is incorrect
Questions 1-8 use the same data.

The following integers were obtained as the number of visits to a gift shop, per hour, over several days.

 0, 2, 3, 1, 2, 4, 5, 2, 3, 4, 2, 3, 3, 5, 6, 2, 1, 4, 1, 4, 3, 1, 6, 2, 1, 4, 5, 2, 3, 3, 1, 2.

Find the outlier(s) for the above data. Exactly one option must be correct)
 a) There are no outlier(s). b) 0 c) 6 d) -1

Choice (a) is correct!
All of the data points lie between 0 and 6 inclusive, so there are no outliers.
Choice (b) is incorrect
Choice (c) is incorrect
Choice (d) is incorrect
The 5-figure summary of a sample of data is:

$88.6\phantom{\rule{2em}{0ex}}90.4\phantom{\rule{2em}{0ex}}91.6\phantom{\rule{2em}{0ex}}92.7\phantom{\rule{2em}{0ex}}94.7$
What is the interquartile range (IQR)?

Correct!
${Q}_{3}=92.7$ and ${Q}_{1}=90.4$ so IQR$=92.7-90.4=2.3$.
Which figures in the summary are the first and third quartiles?
The following measurements (in mm) were taken (to a very high degree of accuracy) for the expansion of sections of railway track on days when the temperature exceeded 35${}^{o}$C. They were distributed into the following intervals, with the indicated frequencies.

 Cell boundary Frequency 0 to $<$0.1 3 0.1 to $<$0.2 5 0.2 to $<$0.3 10 0.3 to $<$0.4 8 0.4 to $<$0.5 6 0.5 to $<$0.6 4 0.6 to $<$0.7 3 0.7 to $<$0.8 2

How would you describe the above distribution? Exactly one option must be correct)
 a) Left skewed. b) Right skewed. c) Symmetrical. d) Uniform.

Choice (a) is incorrect
Choice (b) is correct!
The distribution has a long right tail.
Choice (c) is incorrect
Choice (d) is incorrect