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In a certain sample of data, mean is 23 and standard deviati
[#permalink]
31 Dec 2021, 01:50

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Question Stats:

In a certain sample of data, mean is 23 and standard deviation is 3.5. Which of the following values are less than 2 standard deviation from the mean?

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

Posted from my mobile device

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

Posted from my mobile device

Re: In a certain sample of data, mean is 23 and standard deviati
[#permalink]
31 Dec 2021, 09:35

Expert Reply

In my opinion the answers are wrong

The SD is 3.5 + 2 values = 5.5

The data point OR are above the mean + the 5.5 OR less than 23-5.5

So our values are OR above 28.5 OR less 17.5

So the answers should be from A >>> D

The SD is 3.5 + 2 values = 5.5

The data point OR are above the mean + the 5.5 OR less than 23-5.5

So our values are OR above 28.5 OR less 17.5

So the answers should be from A >>> D

In a certain sample of data, mean is 23 and standard deviati
[#permalink]
01 Jan 2022, 06:27

1

Sumukh19 wrote:

In a certain sample of data, mean is 23 and standard deviation is 3.5. Which of the following values are less than 2 standard deviation from the mean?

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

----------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 = (1)(4) = 4

2 standard deviations = (2)(4) = 8

3 standard deviations = (3)(4) = 12

1.5 standard deviations = (1.5)(4) = 6

0.25 standard deviations = (0.25)(4) = 1

etc

------------------------------------------

So, if the mean of the sample is 23, and the standard deviation is 3.5, then:

2 standard deviations ABOVE the mean = 23 + 2(3.5) = 30

2 standard deviations BELOW the mean = 23 - 2(3.5) = 16

So, values that are LESS THAN 2 standard deviation from the mean, will be all values between (but not including) 16 and 30

Answer: D, E, F

_________________

Re: In a certain sample of data, mean is 23 and standard deviati
[#permalink]
01 Jan 2022, 07:16

Expert Reply

GreenlightTestPrep wrote:

Sumukh19 wrote:

In a certain sample of data, mean is 23 and standard deviation is 3.5. Which of the following values are less than 2 standard deviation from the mean?

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

A. 14

B. 15

C. 16

D. 17

E. 18

F. 28

----------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 = (1)(4) = 4

2 standard deviations = (2)(4) = 8

3 standard deviations = (3)(4) = 12

1.5 standard deviations = (1.5)(4) = 6

0.25 standard deviations = (0.25)(4) = 1

etc

------------------------------------------

So, if the mean of the sample is 23, and the standard deviation is 3.5, then:

2 standard deviations ABOVE the mean = 23 + 2(3.5) = 30

2 standard deviations BELOW the mean = 23 - 2(3.5) = 16

So, values that are LESS THAN 2 standard deviation from the mean, will be all values between (but not including) 16 and 30

Answer: D, E, F

Now I got where I did wrong

gmatclubot

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