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The mean of a set of data with a standard deviation of 0.32
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20 Mar 2019, 23:49
20 Mar 2019, 23:49
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The mean of a set of data with a standard deviation of 0.32 is 4.45.
Which of the following numbers fall between 2 and 3 standard deviations away from the mean?
Indicate all possible values.
A. 3.56
B. 3.80
C. 3.84
D. 5.10
E. 5.44
Which of the following numbers fall between 2 and 3 standard deviations away from the mean?
Indicate all possible values.
A. 3.56
B. 3.80
C. 3.84
D. 5.10
E. 5.44
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The mean of a set of data with a standard deviation of 0.32
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21 Mar 2019, 07:45
21 Mar 2019, 07:45
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Carcass wrote:
The mean of a set of data with a standard deviation of 0.32 is 4.45.
Which of the following numbers fall between 2 and 3 standard deviations away from the mean?
Indicate all possible values.
A. 3.56
B. 3.80
C. 3.84
D. 5.10
E. 5.44
Which of the following numbers fall between 2 and 3 standard deviations away from the mean?
Indicate all possible values.
A. 3.56
B. 3.80
C. 3.84
D. 5.10
E. 5.44
------ASIDE-------------------
A little extra background on standard deviations above and below the mean
If, for example, a set has a standard deviation of 4, then:
1 standard deviation = 4
2 standard deviations = 8
3 standard deviations = 12
1.5 standard deviations = 6
0.25 standard deviations = 1
etc
So, if the mean of a set is 9, and the standard deviation is 4, then:
2 standard deviations ABOVE the mean = 17 [since 9 + 2(4) = 17]
1.5 standard deviations BELOW the mean = 3 [since 9 - 1.5(4) = 3]
3 standard deviations ABOVE the mean = 21 [since 9 + 3(4) = 21]
etc.
----------------------------------
GIVEN: The mean of a set of data with a standard deviation of 0.32 is 4.45.
2 standard deviations ABOVE the mean = 4.45 + 2(0.32) = 5.090
3 standard deviations ABOVE the mean = 4.45 + 3(0.32) = 5.410
So, number that fall between 2 and 3 standard deviations ABOVE the mean are between 5.090 and 5.410
Answer choice D falls within this range
2 standard deviations BELOW the mean = 4.45 - 2(0.32) = 3.810
3 standard deviations BELOW the mean = 4.45 - 3(0.32) = 3.490
So, number that fall between 2 and 3 standard deviations BELOW the mean are between 3.490 and 3.810
Answer choices A and B fall within this range
Answer: A, B, D
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The mean of a set of data with a standard deviation of 0.32
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21 Jul 2021, 06:31
21 Jul 2021, 06:31
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We are given Mean = 4.45 and Standard Deviation(SD) = 0.32 and we need to find which of the following numbers fall between 2 and 3 standard deviations away from the mean
Now, lets calculate the value which defines the range of (mean+2SD and mean+3SD) and (mean-2SD and mean-3SD)
Mean + 2*SD = 4.45 + 2*0.32 = 4.45 + 0.64 = 5.09
Mean + 3*SD = 4.45 + 3*0.32 = 4.45 + 0.96 = 5.41
Mean - 2*SD = 4.45 - 2*0.32 = 4.45 - 0.64 = 3.81
Mean - 3*SD = 4.45 - 3*0.32 = 4.45 - 0.96 = 3.49
So, we need to look for values between (5.09 and 5.41) and (3.49 and 3.81)
So, 3.56, 3.80 and 5.10 are the values
So, Answer will be A,B and D
Hope it helps!
Watch the following video to Learn the Basics of Statistics
Now, lets calculate the value which defines the range of (mean+2SD and mean+3SD) and (mean-2SD and mean-3SD)
Mean + 2*SD = 4.45 + 2*0.32 = 4.45 + 0.64 = 5.09
Mean + 3*SD = 4.45 + 3*0.32 = 4.45 + 0.96 = 5.41
Mean - 2*SD = 4.45 - 2*0.32 = 4.45 - 0.64 = 3.81
Mean - 3*SD = 4.45 - 3*0.32 = 4.45 - 0.96 = 3.49
So, we need to look for values between (5.09 and 5.41) and (3.49 and 3.81)
So, 3.56, 3.80 and 5.10 are the values
So, Answer will be A,B and D
Hope it helps!
Watch the following video to Learn the Basics of Statistics
