The distribution of 27 salaries at a small company has mean $35,000 and standard deviation $2,000. Suppose the company hires a 28th
28th employee at a salary of $120,000. Which of the following claims about the new salary distribution is supported?
The median is not likely to change. I
The range is not likely to change. II
The mean is likely to increase. III
A I only
B III only
C I and II only
D I and III only
E I, II, and III
A?
The following boxplot summarizes the heights of a group of people who participate in a weekend biking club.
The figure presents a boxplot above a number line. The number line is labeled Height, in inches, and the numbers 60 through 76, in increments of 2, are indicated. The boxplot is described as follows. The left whisker extends from 61 inches through 62 inches. The box extends from 62 inches through 70 inches, and a vertical line segment at 67 inches breaks the box into two parts. The right whisker extends from 70 inches through 73 inches.
Which of the following statements is supported by the boxplot?
The mean height is 67 inches.
A
The number of people with height at least 70 inches is greater than the number of people with height at most 62 inches.
B
The number of people with height at least 67 inches is less than the number of people with height at most 67 inches.
C
Approximately 50% of the people have a height between 62 inches and 70 inches.
D
Approximately 25% of the people have a height greater than 62 inches.
E
C??
The following table shows statistics on the ages, in years, of the people who attended a lecture last week. The data are summarized in the boxplot shown.
N 45
Mean 43 StDev 12
Minimum 20 Q1 33
Median 44 Q3 53
Maximum 65
The figure presents a boxplot above a number line titled, Age of People Attending Lecture, and the numbers 10 through 70, in increments of 10, are indicated. The box plot is described as follows. The left whisker extends from 20 years old through 33 years old. The box extends from 33 years old through 53 years old, and a vertical line segment at 44 years old breaks the box into two parts. The right whisker extends from 53 years old through 65 years old.
Which of the following statements is supported by the table and boxplot?
The range of the distribution is 20 years.
A
There were 43 people who attended the lecture.
B
At least 50% of the people who attended the lecture were 43 years or younger.
C
At least 75% of the people who attended the lecture were age 53 years or younger.
D
At least 25% of the people who attended the lecture were 33 years old.
E
My answer Choices 1. A , 2. B 3. E?
Okay so #1 is B only the mean is likely to increase, while the median and range also increase.
Number one is D because it wants you to identify that the median is not affected by outliers but the mean is. That's why it uses "not likely" and "likely."
I am not going to go through all this but immediately question your answer to the first one.
You had 27 employees
so
13 were below median
the 14 th was median
13 were above median
NOW you add a 28 th employee with a much bigger salary
now you have 14 below median and 14 above median
SO the median is now halfway between the 14th and the 15 th.
It changed.
120,000 is much more than a standard deviation above the mean, I bet it is the highest and therefore the range likely increased.
It is way above the mean. Of course it changed the mean.
Did you read the question?
For the first question, the distribution of salaries at a small company has a given mean and standard deviation. Suppose the company hires a new employee at a significantly higher salary. We need to determine which claims about the new salary distribution are supported.
To answer this question, we need to understand the effects of adding an outlier (in this case, the 28th employee with a salary of $120,000) on different measures of central tendency and dispersion.
I. The median is not likely to change:
The median represents the middle value in a dataset. Adding a single outlier does not affect the position of the middle value, so the median is likely to remain the same.
II. The range is not likely to change:
The range is the difference between the maximum and minimum values in a dataset. The new maximum value of $120,000 would increase the range, so this claim is not supported.
III. The mean is likely to increase:
The mean is susceptible to outliers because it takes into account all the values in a dataset. In this case, the new employee's salary is significantly higher than the previous salaries, so the mean is likely to increase.
Based on the explanations above, the correct answer to this question is B) III only.
For the second question, the boxplot summarizes the heights of a group of people who participate in a weekend biking club.
The boxplot provides information on the quartiles, median, and the range of the dataset. We need to determine which of the given statements is supported by the boxplot.
The statement "The mean height is 67 inches" cannot be supported by the boxplot because it does not provide information about the mean.
The statement "The number of people with height at least 70 inches is greater than the number of people with height at most 62 inches" cannot be determined from the boxplot alone. The boxplot does not directly provide information about quantities.
The statement "The number of people with height at least 67 inches is less than the number of people with height at most 67 inches" cannot be supported either. The boxplot does not provide exact counts or ratios.
The statement "Approximately 50% of the people have a height between 62 inches and 70 inches" can be supported by the boxplot since the box represents the interquartile range (IQR), which includes the middle 50% of the data.
Therefore, the correct answer is D) Approximately 50% of the people have a height between 62 inches and 70 inches.
For the third question, the table provides statistics on the ages of people who attended a lecture, and the boxplot summarizes the same data.
The range of the distribution is defined as the difference between the minimum and maximum values. In this case, the range is 65 - 20 = 45 years, so statement A is correct.
The table indicates that there were 45 people who attended the lecture, so statement B is incorrect.
The boxplot does not directly provide information about specific percentages but allows us to estimate them approximately. Since the box represents the interquartile range (IQR), approximately 50% of the people who attended the lecture were younger than or equal to 53 years old. Thus, statement C is incorrect.
Similarly, at least 75% of the people who attended the lecture were younger than or equal to 53 years old since the box ends at that point. Therefore, statement D is correct.
Lastly, the boxplot does not provide information about specific ages, such as 33 years old. Hence, statement E is incorrect.
Therefore, the correct answer is Choices 1. A, 2. B, and 3. D.