- A Since the set has an even number of items, the median is the average of the
two middle terms: 5 + 9 2 = 7. The average of the set is 2 + 3 + 5 + 9 + 11 + 6 x =
30 + x
6. You are told that the average equals the median, so:
30 + 6 x = 7
30 + x = 42
x = 12 - A the revenue for the entire year = average monthly revenue × number of
months = $20,000 × 12 = $240,000. The revenue for the first 10 months =
average monthly revenue × number of months = $18,000 × 10 = $180,000.
The revenue for the last two months is thus $240,000 – $180,000 = $60,000.
Let n = the revenue in November. Since the revenue in December was 50%
greater than the revenue in November, the revenue in December = 1.5n =^32 n.
Solve for n:
n +^32 n = 60,000
52 n = 60,000
n = 24,000 - 30 The sum of the weights of the crates = A × N = 70 × 3 = 210. Let the weight
of the lightest box = l and the weight of the heaviest box = h. Thus
l + 90 + h = 210
l + h = 120
To maximize the weight of the lightest box, you must minimize the weight of
the heaviest box. Since the heaviest box is to the right of the median, its weight
can be no less than the median weight. Thus the least weight for the heaviest
box = the median = 90. Substitute 90 for h:
l + 90 = 120
l = 30 - C, D, and E The median value of the original set is $300,000. The increase
in the price of the smallest home is too small to affect the median. Eliminate
Choices A and B. The $20,000 increase means that the sum of the set will
increase. If the sum of a set increases and the number of items stay the same,
then the average must increase. Choice C is true. The increase in the smallest
price decreases the spread of all the data points. Thus the standard deviation
will decrease. Choice D is true. The increase in the smallest price will decrease
the distance between the smallest and greatest values in the set. The range will
thus decrease. Choice E is true. - D The median refers to the middle data point when all the data points are in
increasing order. Since there are 25 data points, the median will be the 13th
largest data point (since there are 12 data points below this value and 12 above
it). The bottom 12 data points are in the $100,000; $120,000; and $130,000
columns. The 13th data point is thus in the next column: $170,000. - A Standard deviation is a measure of the typical spread of the data points
from the mean. If all of the data points in a set are increased by the same
CHAPTER 12 ■ FROM WORDS TO ALGEBRA 33704-GRE-Test-2018_313-462.indd 337 12/05/17 12:03 pm