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Consider the sets S, T and U, where S={31,14,64,22,43,66} U={y,31,14,6
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08 Jun 2020, 02:33
08 Jun 2020, 02:33
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Consider the sets S, T and U, where
S = {31, 14, 64, 22, 43, 66},
T = {x, 31, 14, 64, 22, 43, 66}, and
U = {y, 31, 14, 64, 22, 43, 66}
The mean of T is 5 less than the mean of S. The median of U is 4 less than the median of S.
Select the value of x and the value of y consistent with the statements given. Make two selections, one in each column.
S = {31, 14, 64, 22, 43, 66},
T = {x, 31, 14, 64, 22, 43, 66}, and
U = {y, 31, 14, 64, 22, 43, 66}
The mean of T is 5 less than the mean of S. The median of U is 4 less than the median of S.
Select the value of x and the value of y consistent with the statements given. Make two selections, one in each column.
| X | Y | |
| 5 | ||
| 10 | ||
| 22 | ||
| 30 | ||
| 33 | ||
| 35 |
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Official Answer
X: 5
Y: 33
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Re: Consider the sets S, T and U, where S={31,14,64,22,43,66} U={y,31,14,6
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15 Apr 2021, 01:25
15 Apr 2021, 01:25
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Official Explanation
RO1
To find the mean of T, sum the values in the set and divide by the number of values: \(\frac{x+31+14+64+22+43+66}{7} = \frac{x+240}{7}\). Similarly, the mean of S is \(\frac{31+14+64+22+43+66}{6} = \frac{240}{6} = 40.\) Since the mean of T is 5 less than the mean of S, \(\frac{x+240}{7} = 40 – 5 = 35.\) Multiplying each side of the equation by 7, x + 240 = 245. Thus, x= 245 − 240 = 5.
The correct answer is 5.
RO2
To find the median of S, first arrange the values in order: 14, 22, 31, 43, 64, 66. Because there is an even number of values, the median is half the sum of the two middle values: \(\frac{31+43}{2} = 37\). The median of U is 4 less than the median of S, or 33. U contains an odd number of values, so its median must be one of the values. Since 33 is not among the known values in U, it must be the value of y.
The correct answer is 33.
RO1
To find the mean of T, sum the values in the set and divide by the number of values: \(\frac{x+31+14+64+22+43+66}{7} = \frac{x+240}{7}\). Similarly, the mean of S is \(\frac{31+14+64+22+43+66}{6} = \frac{240}{6} = 40.\) Since the mean of T is 5 less than the mean of S, \(\frac{x+240}{7} = 40 – 5 = 35.\) Multiplying each side of the equation by 7, x + 240 = 245. Thus, x= 245 − 240 = 5.
The correct answer is 5.
RO2
To find the median of S, first arrange the values in order: 14, 22, 31, 43, 64, 66. Because there is an even number of values, the median is half the sum of the two middle values: \(\frac{31+43}{2} = 37\). The median of U is 4 less than the median of S, or 33. U contains an odd number of values, so its median must be one of the values. Since 33 is not among the known values in U, it must be the value of y.
The correct answer is 33.
General Discussion
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Re: Consider the sets S, T and U, where S={31,14,64,22,43,66} U={y,31,14,6
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08 Jun 2020, 23:07
08 Jun 2020, 23:07
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S={31,14,64,22,43,66} = (14,22,31,43,64,66)
Mean = 14+22+31+43+64+66/6
Mean = 240/6
Mean = 40
Median = average of middle term of even no. set
Median = 31+43/2
Median = 37
T={x,31,14,64,22,43,66} and => (X,14,22,31,43,64,66)
Mean = 14+22+31+43+64+66+x/7
Mean = 240+X/7
Set T Mean is 5 less than Mean of Set S
Mean S -5 = Mean T
40 -5 = 240+x/7
35*7 = 240+x
245-240 = x
x = 5
U={y,31,14,64,22,43,66} =>(14,22,31,Y,43,64,66)
The median of U is 4 less than the median of S.
Median S = 37
Median U = 37-4 = 33 = Y
(X,Y) = (5,33)
Mean = 14+22+31+43+64+66/6
Mean = 240/6
Mean = 40
Median = average of middle term of even no. set
Median = 31+43/2
Median = 37
T={x,31,14,64,22,43,66} and => (X,14,22,31,43,64,66)
Mean = 14+22+31+43+64+66+x/7
Mean = 240+X/7
Set T Mean is 5 less than Mean of Set S
Mean S -5 = Mean T
40 -5 = 240+x/7
35*7 = 240+x
245-240 = x
x = 5
U={y,31,14,64,22,43,66} =>(14,22,31,Y,43,64,66)
The median of U is 4 less than the median of S.
Median S = 37
Median U = 37-4 = 33 = Y
(X,Y) = (5,33)
