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题目内容
At least one of each number 3, 6, 8 and 11 is included in a set of 10 numbers. If the median and the mean of the set of numbers are the same, then at most how many 11 can be included in the set?
Among 5 entries in a mailing list, each entry ranges from 55 to 70, inclusive. If the median of these entries is 60, then what is the range of their average?
Among 75 numbers, 18 is included only once.

The number of numbers less than 18 is the same as the number of numbers greater than 18.

Quantity A

The average of these numbers

Quantity B

The median of these numbers
For a group of 9 steel beams stored together, the average (arithmetic mean) length of the beams is 7.2 meters and the median length is 8.4 meters. Two additional steel beams-one that is longer than all 9 beams and one that is shorter than all 9 beams-will be stored with the 9 beams. For the combined group of 11 steel beams, the average length is $$m$$ meters and the median length is $$d$$ meters. Which of the following statements must be true?

Indicate all such statements.
The playing times of the 13 songs on a compact disc were measured. The average (arithmetic mean) playing time of the songs is 3.6 minutes, and the median playing time is 3.4 minutes. Which of the following statements must be true?

Indicateall such statements.


The chart shows the distribution of scores on a quiz in a geometry class.

Quantity A

The median of the quiz scores

Quantity B

The mode of the quiz scores
List M consists of 11 numbers, all of which are integers. Each number in M is at least -22 and at most 33, and both -22 and 33 are in M . If the median of the numbers in M is 0 , what is the range of the possible values of the average (arithmetic mean) of the numbers in M ?
The mean of 5, 5, 5, x, x is p, the median is m, while p=m+2. What is the value of x?
A list of numbers include 15, 16, 20, 25, x

Which of the following value(s) of x could ensure that the median of the list of numbers is greater than the average of the list of numbers?

Indicate all such value(s).
Among 6 different numbers, the average is smaller than the median. The average of the four smallest numbers is 6, while the average of the four greatest numbers is 13.

Quantity A

The average of these numbers

Quantity B

9.5


The frequency distribution above summarizes the numbers of minutes, rounded to the nearest integer, that 46 students individually spent studying for an exam. Based on the information given, which of the following statements must be true?

Indicate all such statements.
Stores A, B, C, and D sell a certain model of printer for the same retail price. The retail price of the printer is discounted by 10 percent, 20 percent, 16 percent, and 12 percent at Stores A, B, C, and D, respectively. If the retail price of the printer is at least $100, which of the following statements about the discounted prices at the four stores must be true?

Indicate all such statements.


In the three frequency distributions, the variable x has integer values from 1 through 5. For which of the distributions is the average (arithmetic mean) of the 15 values of x equal to the median of the 15 values of x?
1, 2, 4, 8, 16......

The first five terms of an infinite sequence are shown above. Each term after the first term is 2 times the preceding term.

n is an odd integer greater than 50.

Quantity A

The average (arithmetic mean) of the first n terms of the sequence

Quantity B

The median (arithmetic mean) of the first n terms of the sequence


Data set D consists of 35 values, all of which are integers. The frequency distribution of the values in D is shown in the histogram, where each interval shown contains values that are greater than or equal to the left endpoint but less than the right endpoint.

Quantity A

The average (arithmetic mean) of the values in D

Quantity B

The median of the values in D
23, 21, 20, 32, 34, 35, 26, 31, 30, 24

For which integer in the list above are 90 percent of the integers in the list less than that integer?
For a certain set of data, 80 is at the 66th percentile, 60 is at the 56th percentile.

Quantity A

The value at the 46th percentile in the set

Quantity B

40
In the distribution of measurements of the variable x, the mean is 56 and the measurement r lies between the 65th and 70th percentiles. In the distribution of measurements of the variable y, the mean is 56 and the measurement t lies between the 75th and 80th percentiles.

Quantity A

r

Quantity B

t
In a random distribution, the value of 42nd, 48th, 54th, and 60th percentile is x, y z, and w, respectively.

Quantity A

y-x

Quantity B

w-z
Number A is the $$90^{th}$$ percentile in set L and number B is the $$70^{th}$$ percentile in set M. Which of the following statements must be true?

Indicate all such statements.

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