Download 28, 165, 168, 170, 172, 190, 192, 195, 202, 220

Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
1. Swimming is one of the major sports in the Summer Olympics. Using the table given below, find the women’s
event from 2012 with the largest spread in
actual times for the event:
A.
B.
C.
D.
E.
50 Free
200 IM
800 Free
100 Back
None of these Answers
2. Synchronized swimming is a fairly new
sport to the Summer Olympics, it began in
1984 in Los Angeles. It was replaced in
1996 by water ballet. Since the 2000 games,
it has been included. Along with Rhythmic
gymnastics, it is the only sport exclusively for women in the Olympics. The first Olympics in the Modern Era was
in 1896 in Athens, Greece. Assuming there was an Olympics every four years since then, find the probability that
Synchronized Swimming was an event at any selected Summer Olympics including Rio 2016.
A. 8⁄31
B. 7⁄31
C. 4⁄15
D. 7⁄30
E. None of these Answers
3. In Olympic diving, the springboard is a flexible diving board that can be adjusted to create more or less spring. It
must be at least 4.8 meters long and a half-meter wide. The springboards being used at the 2016 Rio Summer
Olympics have a known mean spring of 30 cm and a standard deviation of 1.8 cm. Assuming they have a normal
distribution, find the spring length to the nearest tenth that represents the 84th percentile of springboards at the
2016 Rio Olympics.
A. 28.2 cm
D. 33.8 cm
B. 31.8 cm
E. None of these Answers
C. 33.6 cm
4. Using the Scatterplot below, as well as the line of best fit
that is drawn onto it, name the country best described as
an influential observation:
A. China
B. Japan
C. USA
D. Germany
E. None of these Answers
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
5. Using the graph provided, choose the best
answer:
A. The association between time and the year
appears to have a positive association for the
Men’s 100m Freestyle.
B. The correlation between time and the year
appears to be weak for the Men’s 100 m
Freestyle.
C. Using this information to predict times for
2016 Olympics would be interpolation.
D. The correlation of time and the year for the
Men’s 100m Freestyle appears to be closer
-1 than 1.
E. None of these Answers
the
to
6. Tom Brady wants to join the US Olympic Water Polo team. The ball used in water polo weighs between 400 and
450 grams. If Tom prefers his game ball slightly underinflated at the 8th percentile, what is the mass in grams of
the ball Tom prefers? Assume the balls follow a normal distribution. Round to the nearest ten grams.
A. 400
D. 440
B. 410
E. None of these Answers
C. 420
7. Using this _______, you should be able
find the Country with the largest
percentage of silver medals to be ____.
A. Segmented Bar Chart, China
B. Segmented Bar Chart, Germany
C. Histogram, China
D. Frequency Diagram, Russia
E. None of these Answers
to
8. Using the scatterplot below, describe the direction, form and strength of the relationship between training hours
and calories for Olympic swimmers.
A.
B.
C.
D.
E.
Positive direction, Linear, Somewhat weak
Positive direction, Non-Linear, Strong
Negative direction, Linear, Somewhat weak
Positive direction, Non-Linear, Very Strong
None of these Answers
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
9. The data on one Olympic Swimming event is given in the table
below. Use the data to write the Least Squares Regression Line
the time to finish the race as a function of the years past 1920.
What point is guaranteed to be on the regression line? Round
values to the nearest hundredth.
A. (4, 362.2)
B. (44.22, 284.41)
C. (44, 283.30)
D. No points are guaranteed to be on the line
E. None of these Answers
for
10. A synchronized swimmer can hold their breath up to 3 minutes on average. To give you perspective, a dolphin
can hold their breath about 9 minutes, and a grey seal can hold theirs about an hour and a half. A sample was
taken of Olympic synchronized swimmers and their time holding their breath recorded. What are the outliers in
this sample? Use the IQR Method to determine. All times measured in seconds.
28, 165, 168, 170, 172, 190, 192, 195, 202, 220
A.
B.
C.
D.
IQR=27 and the Outlier is 220
IQR=192 and the Outlier is 28
IQR=27 and there are no Outliers
IQR=192 and there are no Outliers
E. None of these Answers
11. Competitive diving, which developed from gymnastics, started in Sweden and Germany
in the 18th century. Known as the greatest diver of all time, American Greg Louganis is
“board” one day and takes a sample of his times to hit the water from the diving board.
Using the sample of times (in seconds) given below, find the appropriate measure of
spread for the distribution.
0.121 , 0.234 , 0.367 , 0.444 , 0.512 , 0.676 , 0.876 , 0.888 , 0. 904 , 0.924 , 1.001 , 1.245
A. M=0.776 because the distribution is
symmetric
B. M=0.776 because the distribution is leftskewed
C. 𝑥̅ = 0.683 because the
distribution is not symmetric
12. What can be concluded from the chart
below about Michael Phelps?
A. Michael Phelps won twice the number
of gold medals between 2004-2012 as
the United Kingdom.
B. Michael Phelps won more gold medals
from 2004-2012 than exactly 8
countries.
D. 𝑥̅ = 0.683 because the distribution is
left-skewed
E. None of these Answers
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
C. This is a bar chart because the medalists is a qualitative variable.
D. Michael Phelps is in the 45th percentile for gold medals in 2004-2012.
E. None of these Answers
13. Speaking of Michael Phelps, the following modified box and whisker plot shows how fast one of the world's greatest
Olympic swimmers, has swum the 200-meter freestyle event (rounded to the nearest second). Which of the following is
NOT correct according to the data below?
A. 108 seconds is the Upper Quartile.
B. The Interquartile Range of the distribution is less than 4 seconds.
C. 103 is the Lower Quartile and the minimum value.
D. There are no outliers in this distribution.
E. None of these Answers
14. Using the data table, find the probabilities:
2016 Olympians
Swimming
USA
China
Russia
88
75
90
A.
B.
C.
497
1275
56
497
521
1275
Diving
Synchronized
Swimming
24
16
28
20
20
32
𝑃(𝑈𝑆𝐴|𝐷𝑖𝑣𝑖𝑛𝑔) + 𝑃(𝑊𝑎𝑡𝑒𝑟 𝑃𝑜𝑙𝑜)
D.
Water Polo
15
15
2
99
497
E. None of these Answers
15. Using the information from the table on problem 14, determine if the number of Olympic athletes in each sport is
independent of country. Choose the best answer below.
A. Yes, because the country you are from does not affect the sport you play.
B. Yes, because the country you are from does affect the sport you play.
C. No, because the probabilities of playing each sport are equal for each country.
D. No, because the probabilities of playing each sport are different for each country.
E. None of these Answers
16. Water polo made its Olympic debut at the Paris Games in 1900. It was not included in 1904 but would be present
at each subsequent edition of the Olympic Games. Since then, the Hungarians have been by far the greatest
ambassadors of this discipline. Between 1928 and 1980, they won medals at every Games. Between 1932 and
1976, they even won six of the 10 gold medals available. In 2000 in Sydney, Hungary make a remarkable
comeback, winning its seventh gold medal in water polo. In the same year, women’s water polo made its first
official appearance at the Olympic Games, 100 years after the debut of this discipline. From the paragraph above,
choose the best example of a quantitative variable:
A. 1928
B. Water Polo
C. Olympic Games
D. Number of Gold Medals
E. None of these Answers
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
17. Women’s swimming became Olympic in 1912 at the Stockholm Games. Since then, it has been part of every
edition of the Games. The men’s and women’s programs are almost identical, as they contain the same number of
events, with only one difference: the freestyle distance is 800 meters for women and 1,500 meters for men. Can
the two sets of all events for men and women swimmers (their programs) in the Olympics be considered disjoint?
Explain why or why not.
A. Yes, men and women can’t swim in the same events, so they must be disjoint.
B. Yes, because the freestyle distance is different for men and women.
C. No, most of the events for men and women swimmers are the same.
D. No, men can race in more than one event.
E. None of these Answers
18. For Olympic Synchronized swimming, the pool must be a minimum of 20 m by 30 m, and within that a 12 m by
12 m area must be at least 3 m deep. The water temperature must be 26 degrees Celsius, plus or minus one degree.
If Olympic pools for synchronized swimming have a normal distribution with a 27 degree Celsius pool having a z
score of 3, find the maximum temperature of the pool in the 92nd percentile. Round to the nearest hundredth
degree Celsius.
A. 26.47
D. 31.22
B. 27.47
E. None of these Answers
C. 30.22
19. Which of the following is NOT true about this graph?
A. The legend is labeled as “Gold Medals” indicating the bars
in the bar graph represent gold medals awarded to each
country.
B. The area principle is violated on this graph to make United
States appear superior.
C. The y-axis is missing a label, but we know the numbers
represent frequency in a bar graph.
D. The countries listed on the x-axis of the graph represent the
categorical variable “Country”.
E. None of these Answers
20. Use the following table to determine if there is a correlation between Total Swim Time and Ave Swim Pace.
Describe the relationship.
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
A. The relationship is very non-linear. The correlation is weak at -0.33. There is almost no association between
total swim time and their average swim pace.
B. The relationship is fairly linear. The correlation is weak at -0.33. There is little association between total swim
time and their average swim pace.
C. The relationship is fairly linear. The correlation is -0.90 seconds. There is an association between total swim
time and their average swim pace.
D. The relationship is fairly linear. The correlation is -0.90. There is a linear association between total swim time
and their average swim pace.
E. None of these Answers
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Statistics Individual – January 16, 2016 – FAMAT State-Wide Competition hosted by Vero Beach HS
Solutions:
1 B or C
2A
3B
4C
5D
6 A or B
7 B or E
8A
9B
10 E
11 E
12 C
13 A
14 C
15 D
16 D
17 A or C
18 A
19 B
20 D
You can see from the table provided that the largest standard deviation is 3.28.
By looking at the arithmetic sequence, the following equation can be used to find the number of Olympic
Games since 1896. 2016 = 1896 + 4𝑥; 𝑥 = 30 That makes 31 games total, and 8 with Synchronized
Swimming (1984, 1988, 1992, 2000, 2004, 2008, 2012, 2016) The probability is then 8/31.
By using the empirical rule, the 84th percentile is exactly one standard deviation about the mean.
30+1.8=31.8 cm
Influential Observations are defined to be extreme outliers in the x-direction. They pull the line of best fit
towards them.
The correlation between the variables is most likely negative because of the direction of the data points.
Knowing the area to the left of the data value is 8%, the mean is 425, and SD is 25/3, we can use the
INVnorm function on the calculator to find: X=413.3, but rounded to the nearest ten is 410.
Germany has 19/44=43% silver medals.
Positive direction is because as the x’s go up, so do the y’s for the majority of values, Linear because is
follows a fairly linear pattern, Somewhat weak because the correlation will most likely be low.
The point (x bar, y bar) is guaranteed to be on the Least Squares Regression Line. Find the average of
each list and that point is (44.22, 284.41).
The IQR is 27, which makes the outlier 28.
M=0.776 because the distribution is left-skewed. Any time that a distribution is skewed, the proper
measure of center is the median. You can tell this distribution is left-skewed because the box plot is
larger on the left side of the median. Also, the median is more than the mean, which indicates the mean is
being pulled to the tail on the left. (Median is not a measure of spread)
This is a bar chart because the variable of interest is qualitative. Histograms are used for quantitative
data.
108 is the maximum.
24/72 + 32/425=521/1275 (To find a probability of USA given Diving, you find the number of athletes
who are from the USA who dive, and then divided by the number who are Divers.
Because all of the conditional probabilities do not match, the variables are NOT independent.
Quantitative variables are numerical values that describe an individual.
The events for men and women are almost identical. Therefore they cannot be disjoint, where there are
no events that overlap.
To find the mean, you use the information given and it is 26. To find the standard deviation, use the z27−26
score given to solve: 3 = 𝜎 Invnorm(0.92,26,1/3)=26.468
The area principle says that all values on a graph should be in their true proportions. There is a consistent
scale on the graph so that is not an issue.
By using the linreg function on the calculator, I found the correlation to be -0.90. The scatterplot looks
like a negative linear association. “C” is incorrect because the units on the correlation.
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