sandy wrote:
The range of the heights of the female students in a certain class is 13.2 inches, and the range of the heights of the male students in the class is 15.4 inches.
Which of the following statements individually provide(s) sufficient additional information to determine the range of the heights of all the
students in the class?
Indicate all such statements.
A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.
B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.
C. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.
A. The tallest male student in the class is 5.8 inches taller than the tallest female student in the class.Let
M = the height of the TALLEST male
This means
M - 5.8 = the height of the TALLEST female
The range of the heights of the females is 13.2 inchesSo,
M - 5.8 - 13.2 = the height of the SHORTEST female
Simplify:
M - 19 = the height of the SHORTEST female
The range of the heights of the males is 15.4 inchesSo,
M - 15.4 = the height of the SHORTEST male
Since
M - 19 = the height of the SHORTEST female, and
M - 15.4 = the height of the SHORTEST male, we can conclude that M - 19 = the height of the SHORTEST STUDENT
We also know that
M = the height of the TALLEST STUDENT
So, the range = (height of the TALLEST STUDENT) - (height of the SHORTEST STUDENT)
=
M - (
M - 19)
= 19
So, the range of all student heights is 19 inches
So,
statement A provides SUFFICIENT information to determine the range of all heights.
B. The median height of the male students in the class is 1.1 inches greater than the median height of the female students in the class.This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):
Case a: The heights of the males are {
50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females is {
40, 52.1, 53.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {40, 50, 51, 52.1, 53.2, 65.4}
So,
the range of all heights = 65.4 - 40 = 25.4 inchesCase b: The heights of the males are {
50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEDIAN height is 51 inches)
The heights of the females are {
50, 52.1, 63.2} (notice that the range of heights is 13.2 inches). Here, the MEDIAN height is 52.1 inches)
In this case, the heights of ALL students are: {50, 50, 51, 52.1, 53.2, 65.4}
So,
the range of all heights = 65.4 - 50 = 15.4 inchesSince the range can be 25.4 inches OR 15.4 inches,
statement B does NOT provides suffient information to determine the range of all heightsC. The average (arithmetic mean) height of the male students in the class is 4.6 inches greater than the average height of the female students in the class.This is NOT sufficient information.
Consider these two possible cases (since we're aren't told the number of males and females, let's say there are 3 male students and 3 female students):
Case a: The heights of the males are {
50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {
45, 49.5, 58.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {45, 49.5, 50, 51, 58.2, 65.4}
So,
the range of all heights = 65.4 - 45 = 20.4 inchesCase b: The heights of the males are {
50, 51, 65.4} (notice that the range of heights is 15.4 inches). Here, the MEAN height is 55.5 inches)
The heights of the females is {
44, 51.5, 57.2} (notice that the range of heights is 13.2 inches). Here, the MEAN height is 50.9 inches)
In this case, the heights of ALL students are: {44, 51.5, 50, 51, 57.2, 65.4}
So,
the range of all heights = 65.4 - 44 = 21.4 inchesSince the range can be 20.4 inches OR 21.4 inches,
statement C does NOT provides suffient information to determine the range of all heightsKEY CONCEPT: Knowing the range of two different populations AND knowing the relative sizes of those populations' median or mean is not enough to determine the range of the COMBINED populations.
Cheers,
Brent
Knowing the range of two different populations AND knowing the relative sizes of those populations' median or mean is not enough to determine the range of the COMBINED populations.