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In a certain sample of data, mean is 23 and standard deviation is 3.5.
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27 Jul 2023, 06:33
27 Jul 2023, 06:33
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In a certain sample of data, the mean is 23 and the standard deviation is 3.5. Which of the following values are less than 2 standard deviations from the mean?
Indicate all that apply
A. 14
b. 15
C. 16
D. 17
E. 18
F. 28
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Indicate all that apply
A. 14
b. 15
C. 16
D. 17
E. 18
F. 28
Post A Detailed Correct Solution For The Above Questions And Get Kudos.
Question From Our Project: Free GRE Prep Club Tests in Exchange for 20 Kudos
\(\Longrightarrow\) GRE - Quant Daily Topic-wise Challenge
\(\Longrightarrow\) GRE Math Essentials - A most comprehensive handout!!
\(\Longrightarrow\) Free Materials for the GRE General Exam - Where to get it!!
\(\Longrightarrow\) Best GRE Test Books of 2023
Re: In a certain sample of data, mean is 23 and standard deviation is 3.5.
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17 Sep 2023, 02:10
17 Sep 2023, 02:10
Expert Reply
OE
.It is given that mean = 23 and standard deviation = 2.5
We have to find the values which are less than 2 standard deviations from the mean.
We know that, deviation of the terms from the mean can be on both the sides, either
less than the mean or more than the mean
Where, M = Mean
D = Standard Deviation
m, if we see the points marked on the right of mean, all the
points are at a deviation of less than 2D. So that’s why, any point lying between M
and M + 2D will be having its deviation less than 2 standard deviations from the
mean value.
Similarly
If we take from M-2D to M, we see the points marked on the left of the mean, all the
points are at a deviation of less than 2D. So that’s why, any point lying between M
and M - 2D will be having its deviation less than 2 standard deviations from the mean
value.
Now, as per the question, M = 23
And, D = 3.5
So, 2 standard deviation = 2D = 7
So, the values 16 and 30 are exactly 2 standard deviations away from the mean.
But we are looking for those values which are less than 2 standard deviations from
the mean.
So, it can take any value between 16 and 30.
Hence, the possible values as per the options will be 17, 18 and 28.
Ans. (D, E, F)
.It is given that mean = 23 and standard deviation = 2.5
We have to find the values which are less than 2 standard deviations from the mean.
We know that, deviation of the terms from the mean can be on both the sides, either
less than the mean or more than the mean
Where, M = Mean
D = Standard Deviation
m, if we see the points marked on the right of mean, all the
points are at a deviation of less than 2D. So that’s why, any point lying between M
and M + 2D will be having its deviation less than 2 standard deviations from the
mean value.
Similarly
If we take from M-2D to M, we see the points marked on the left of the mean, all the
points are at a deviation of less than 2D. So that’s why, any point lying between M
and M - 2D will be having its deviation less than 2 standard deviations from the mean
value.
Now, as per the question, M = 23
And, D = 3.5
So, 2 standard deviation = 2D = 7
So, the values 16 and 30 are exactly 2 standard deviations away from the mean.
But we are looking for those values which are less than 2 standard deviations from
the mean.
So, it can take any value between 16 and 30.
Hence, the possible values as per the options will be 17, 18 and 28.
Ans. (D, E, F)
Re: In a certain sample of data, mean is 23 and standard deviation is 3.5.
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09 Jan 2024, 07:57
09 Jan 2024, 07:57
1
Carcass Sir, if it has been asked to find values that are less than 2 standard deviations below the mean?
then we would choose all the options , right ?
but as nothing like below or above the mean is given , we have consider the range of value for 2 standard deviations from the mean , right ?
then we would choose all the options , right ?
but as nothing like below or above the mean is given , we have consider the range of value for 2 standard deviations from the mean , right ?
