sandy wrote:
In the course of an experiment, 95 measurements were recorded, and all of the measurements were integers. The 95 measurements were then grouped into 7 measurement intervals. The graph above shows the frequency distribution of the 95 measurements by measurement interval.
Quantity A |
Quantity B |
The average (arithmetic mean) of the 95 measurements |
The median of the 95 measurements |
A)The quantity in Column A is greater.
B)The quantity in Column B is greater.
C)The two quantities are equal.
D)The relationship cannot be determined from the information given.
Tough/time-consuming question.
QUANTITY ATo find the mean, we must add all 95 values.
Notice that, that each interval, there are 5 possible values for each data point.
For example, the first entry is 1-5, which means the each of the 15 data points can be 1, 2, 3, 4, or 5 (NOTE: the data points are all INTEGERS)
So, which value do we use?
If all 15 data points are 1, then the mean will be different from the case where are 15 data points are 5.
So, let's see what happens if each data point is the
MINIMUM POSSIBLE VALUE1-5 interval: there are 15 data points. So if each data point is 1, then the SUM = (15)(1) =
156-10 interval: there are 35 data points. So if each data point is 6, then the SUM = (35)(6) =
21011-15 interval: there are 15 data points. So if each data point is 11, then the SUM = (15)(11) =
16516-20 interval: there are 12 data points. So if each data point is 16, then the SUM = (12)(16) =
19221-25 interval: there are 10 data points. So if each data point is 21, then the SUM = (10)(21) =
21026-30 interval: there are 5 data points. So if each data point is 26, then the SUM = (5)(26) =
13031-35 interval: there are 3 data points. So if each data point is 31, then the SUM = (3)(31) =
93So, the SUM of all 95 data points =
15 +
210 +
165 +
192 +
210 +
130 +
93=
1015So, MEAN =
1015/95 ≈ 10.6
Since we used the smallest possible value for each interval, we can conclude that the SMALLEST possible value of Quantity A is 10.6
QUANTITY BThe median of the 95 data points will be the MIDDLEMOST value when all of the values are arranged in ASCENDING ORDER
So, the median will equal the 48th value when all of the values are arranged in ASCENDING ORDER
In the 1-5 interval, there are 15 data points.
In the 6-10 interval, there are 35 data points.
At this point, we've already accounted for 50 data points (15 + 35 = 50).
This means the 48th value will be in the 6-10 interval.
So, the median of the set must be 6, 7, 8, 9, or 10
So, the largest possible value of Quantity B is 10
And, the smallest possible value of Quantity A is 10.6
So, we can be certain that Quantity A is greater.
Answer:
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