Question 1 :
Ages of the First 12 United States Presidents at the Beginning of Their Terms in Office.
The table above lists the ages of the first 12 United States presidents when they began their terms in office. According to the table, what was the mean age, in years, of these presidents at the beginning of their terms? (Round your answer to the nearest tenth.)
Answer :
The mean of a data set is determined by calculating the sum of the values and dividing by the number of values in the data set.
Sum of ages :
= 57+ 62 + 58 + 58 + 59 + 58 + 62 + 55 + 68 + 51 + 50 + 65
= 703
Mean age :
= 703/12
≈ 58.6
Question 2 :
Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple?
A) 4
B) 5
C) 6
D) 7
Answer :
The average number of seeds per apple is the total number of seeds in the 12 apples divided by the number of apples, which is 12.
There are
3 apples with 2 seeds each ----> 3 x 2 = 6 seeds
5 apples with 4 seeds each ----> 5 x 4 = 20 seeds
6 apples with 1 seed each ----> 6 x 1 = 6 seeds
7 apples with 2 seeds each ----> 7 x 2 = 14 seeds
9 apples with 3 seeds each ----> 9 x 3 = 27 seeds
Total number of seeds in 12 apples :
= 6 + 20 + 6 + 14 + 27
= 73
Average number of seeds per apple :
= 73/12
≈ 6.08
Of the choices given, 6 is closest to 6.08.
The correct answer choice is (C).
Question 3 :
A survey was taken of the value of homes in a county, and it was found that the mean home value was $165,000 and the median home value was $125,000. Which of the following situations could explain the difference between the mean and median home values in the county?
A) The homes have values that are close to each other.
B) There are a few homes that are valued much less than the rest.
C) There are a few homes that are valued much more than the rest.
D) Many of the homes have values between $125,000 and $165,000.
Answer :
Median is the middle value of a data.
For the data given, the median is $125,000. So, 50% of the homes are valued less than $125,000 and 50% of the homes are valued more than $125,000.
For any data, mean the best representative all the values in the data.
In the data given, mean is greater than median. So, most of the homes are valued less than the mean and few homes are valued more than the mean.
The correct answer choice is (C).
Question 4 :
An online store receives customer satisfaction ratings between 0 and 100, inclusive. In the first 10 ratings the store received, the average (arithmetic mean) of the ratings was 75. What is the least value the store can receive for the 11th rating and still be able to have an average of at least 85 for the first 20 ratings?
Answer :
Average of the first 10 ratings = 75
(Sum of the first 10 ratings)/10 = 75
Multiply both sides by 10.
Sum of the first 10 ratings = 750
Average of the first 20 ratings = 85
(Sum of the first 20 ratings)/20 = 85
Multiply both sides by 20.
Sum of the first 20 ratings = 1700
Sum of the ratings from 11 to 20 :
= 1700 - 750
= 950
There are ten ratings from 11 to 20.
In these ten ratings from 11 to 20, if the nine ratings from 12 to 20 received the maximum rating 100 each, then the maximum possible value of the sum of the nine ratings (from 12 to 20) is
Therefore, the least possible value for the 11^{th} rating is
= 950 - 900
= 50
Question 5 :
If x is the average (arithmetic mean) of m and 9, y is the average of 2m and 15, and z is the average of 3m and 18, what is the average of x, y, and z in terms of m?
A) m + 6
B) m + 7
C) 2m + 14
D) 3m + 21
Answer :
From the information given,
Average of x, y, and z :
The correct answer choice is (B).
Question 6 :
The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?
A) 20
B) 24
C) 32
D) 36
Answer :
Mean score of 8 players = 14.5
(Sum of the cores of 8 players)/8 = 14.5
Multiply both sides by 8.
Sum of the cores of 8 players = 116
After removing the highest individual score,
mean score of 7 players = 12
(Sum of the cores of 7 players)/7 = 12
Multiply both sides by 7.
Sum of the cores of 7 players = 94
Highest individual score :
= 116 - 94
= 22
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