Sophia Learning
STAT1001: Introduction to Statistics UNIT 2 — MILESTONE 2
24/25 that's 96% RETAKE
1 question was answered incorrectly.
Naomi weighed 50 patients for a medical study using a scale that measures to th
...
Sophia Learning
STAT1001: Introduction to Statistics UNIT 2 — MILESTONE 2
24/25 that's 96% RETAKE
1 question was answered incorrectly.
Naomi weighed 50 patients for a medical study using a scale that measures to the nearest whole pound. She then calculated the mean weight as 176 pounds, with a standard deviation of 12 pounds.
If the distribution is normal, what percent of the data lies between 140 pounds and 212 pounds?
● ●
34%
UNIT 2 — MILESTONE 2
24/25
140 pounds and 212 pounds are both 36 pounds from the mean of 176 pounds, which is the same as three standard deviations (12 pounds * 3) in either direction. This tells us that 99.7% of the data should lie between 140 cm to 212 cm.
● 95%
● 68%
99.7%
Page 2 of 42
2
Ralph records the time it takes for each of his classmates to run around the track one time. As he analyzes the data on the graph, he locates the mean and median time.
Which component of data analysis is Ralph utilizing?
●
●
The overall shape of the data
The center of the data set
●
An outlier in the data set
●
The overall spread of the data
Page 3 of 42
CONCEPT
→ Data Analysis
3
measures of center. So by examining this, Ralph is looking at the center of the data.
Dave drives to work. While driving the car over nine days, he observes his daily average speed and lists it in the table below.
Day Average Speed (MPH)
1 45
2 62
3 44
4 70
5 59
6 66
7 54
8 63
9 67
●
● 58.89 miles per hour
● 63 miles per hour
● 59 miles per hour
62 miles per hour
Page 5 of 42
4
The graph below shows the change in passenger load factor for all scheduled airlines in the United States over different months of a year.
Which segment of the graph indicates no change in the passenger load?
●
● A
B
The dot plot below shows the number of songs Carly downloaded over 15 successive weekends. Each blue dot represents one weekend.
● ●
D
● C
Page 7 of 42
What is the greatest number of songs downloaded on a single weekend?
● 9
10
● 6
● 8
Page 8 of 42
CONCEPT
→ Dot Plots
6
downloaded in a single weekend is 10.
In which of these cases should the median be used?
●
●
When data has no outliers
When the data has extreme values
●
When the data has nominal values
●
When the data has small variance
the median is a better measure since it is not as sensitive to these values.
Which of the following statements is true for an outlier?
●
It is a data point that is below Q1 - 1.5 x IQR or above Q3 + 1.5 x IQR.
Page 10 of 42
CONCEPT
→ Outliers and Modified Boxplots
8
RATIONALE
To find an outlier we note the lower bound and upper bound for outliers are Q1 - 1.5IQR and Q3 + 1.5IQR respectively.
● ●
It is a data point that is below or above Q3 ± 1.5 x IQR.
●
It is a data point that is below or above Q1 ± 1.5 x IQR.
●
It is a data point that is between Q1 + 1.5 x IQR and Q3 - 1.5 x IQR.
Page 11 of 42
Consider the times (in seconds) that it took children and adults to solve a Rubik’s cube at a competition.
What does the circled section represent?
●
One child solved the Rubik's cube in 21.7 seconds.
One child took 72 seconds to solve the Rubik's cube, while another took 71 seconds to solve it.
●
21 children completed the Rubik's cube in 7 seconds.
●
21 children completed the Rubik's cube in 7 minutes.
Page 13 of 42
9
One week, Rachel earned $250. She spent $120 on food, $30 on miscellaneous items, and saved the rest.
If Rachel makes a pie chart showing how she spends her money, the central angle for the food sector would be __________.
●
173°
● 90°
● 144°
● 187°
Page 14 of 42
10
So in this case, the central angle for the food sector would be:
Sara wonders how many of her students answered at least half of the quiz questions incorrectly.
●
Page 15 of 42
The cumulative frequency of students who earned a score of 20 or lower on the quiz is __________.
● 54
68
● 34
This would be:
Consider the histogram showing the weights of babies born in a hospital over a month.
● ●
27
Page 17 of 42
How many babies are less than 6 pounds?
4
● 5
● 12
● 3
12
So there are 4 babies that weigh less than 6 pounds.
The formula for the standard deviation of a sample is:
Select the true statement for the following data set that has a mean of 8:
4, 6, 6, 6, 9, 9, 12, 12
Answer choices are rounded to the hundredths place.
●
●
The variance is 8.86 and the standard deviation is 7.50.
The variance is 8.86 and the standard deviation is 2.98.
●
The variance is 7.50 and the standard deviation is 2.98.
●
The variance is 2.98 and the standard deviation is 8.86.
13
We can also use the statistical functions in Excel to quickly find the variance and standard deviation.
Hannah noted the height of each student in her class and found that the mean height of the students is 56 inches, with a standard deviation of 1.2 inches. The height of one of the students, James, is 59 inches.
What is the z-score for James' height?
● ●
-3.6
● -2.5
14
The given value is 59 inches, the mean is 56 inches, and the standard deviation is 1.2 inches. Plug these values in to get the following z-score:
This also tells us that 59 is 2.5 z-scores or standard deviations above the mean.
● ●
3.6
2.5
Page 22 of 42
You are asked to gather some data on wait times for a popular rollercoaster at the amusement park where you work. You can't track the waiting time of every rider, so you decide to sample 81 people at random each day. The mean of a distribution of sample mean wait times is 18 minutes and the standard deviation of the sampling distribution ( ) is 0.5 minutes.
What is the standard deviation of the population ( )?
4.5
● 0.5
● 18
● 2
Page 23 of 42
CONCEPT
→ Center and Variation of a Sampling Distribution
15
by the square root of the sample size, .
We know the sample standard deviation is 0.5 and the size of the sample is 81, so we can solve for the standard deviation of the population:
A baseball scout recorded the type of pitch a pitcher threw during a game and whether it was thrown for a strike or a ball.
●
Page 24 of 42
Which of the following statements about the stack plot is true?
●
The pitcher threw the changeup the most often.
●
The pitcher's least accurate pitch (lowest percentage of strikes) is the slider.
Page 25 of 42
CONCEPT
→ Stack Plots
16
Select the statement that accurately describes unimodal distribution.
●
The pitcher's least accurate pitch (lowest percentage of strikes) is the curveball.
●
The pitcher threw the curveball most often.
Page 26 of 42
●
A distribution in which numerous values are more frequent than other values.
●
A distribution in which the values are distributed uniformly.
A distribution in which one value is more frequent than other values.
●
A distribution in which two distinct values are more frequent than the other values.
Page 27 of 42
17
At Brent's school, the final grade for his U.S. History course is weighted as follows:
Tests: 30%
Quizzes: 50%
Homework: 20%
Brent has an average of 82% on his tests, 94% on his quizzes, and 50% on his homework.
What is Brent's weighted average?
●
● 74.8%
81.6%
● 75.3%
Page 28 of 42
CONCEPT
→ Weighted Mean
18
Jerry graded seven standardized tests with the following scores:
60, 74, 41, 87, 94, 79, 57
Which standardized test score represents the 50th percentile?
● ●
69.6%
● 41
Page 29 of 42
CONCEPT
→ Percentiles
19
Select the statement that is TRUE.
● ●
79
74
● 57
Page 30 of 42
●
The interquartile range covers 100% of a data set.
●
The interquartile range is calculated by adding the first quartile with the third quartile.
The interquartile range is calculated by subtracting the first quartile from the third quartile.
●
The interquartile range is the average value of a data set.
Page 31 of 42
CONCEPT
→ Range and Interquartile Range (IQR)
20
Which of the following statements is true?
●
A standard normal curve has a mean of 1 and a standard deviation of 1.
A standard normal curve has a mean of 0 and a standard deviation of 1.
●
A standard normal curve has a mean of 1 and a standard deviation of 2.
Page 32 of 42
CONCEPT
21
Jerry, Stein, Johnson, and Mary had a competition to see who could profit the most from their odd jobs during the summer. They discussed their earnings on the first day of school. Stein created the following bar graph to plot the different amounts they earned.
● ●
A standard normal curve has a mean of 0 and a standard deviation of 2.
Page 33 of 42
Which statement explains why the graph is misleading?
●
The scale of intervals on the horizontal axis is inconsistent.
●
The vertical axis should be in terms of hours worked instead of amount earned.
Page 34 of 42
CONCEPT
→ Misleading Graphical Displays
22
Which of the following statements about a normal distribution is true?
● ●
The horizontal axis should be in terms of months instead of names.
The scale of intervals on the vertical axis is inconsistent.
●
A large portion of the data is skewed to the right.
●
The normal distribution is an example of a bimodal distribution.
The normal distribution is singlepeaked and symmetric.
●
A large portion of the data is located near the tails.
23
The first quartile (Q1) value from the above box plot is __________.
●
47
● 40
● 65
● 54
Page 37 of 42
Which of the following statements is true?
●
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the population mean as long as the sample size is large enough.
●
According to the Central Limit Theorem, the mean of the sampling distribution is equal to the standard deviation.
●
According to the Central Limit Theorem, the mean of the sampling distribution is greater than the population mean.
●
According to the Central Limit Theorem, the mean of the sampling distribution is greater than the standard deviation.
Page 39 of 42
25
In a survey to rate the customer service department of a company, 300 persons rated their agreement with the statement, "The staff is helpful and courteous." The information was put into a table.
Rating Frequency
Strongly Agree 32
Agree 50
Neutral 97
Disagree 53
Strongly Disagree 68
The relative frequency of people who strongly disagree with the statement is __________.
● ●
10.7%
● 68%
● 40.3%
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