barca14 wrote:A massage therapist provides sessions that last exactly 27 minutes, but as a reward to his customers, every fifth session is 42 minutes. If every customer comes for a very large number of sessions, what is the standard deviation of the massage time? Round your answer to three decimal places.

Please transfer the question to the suitable forum, moderators.

The massage time (in minute) to a customer runs as below for sessions:

27, 27, 27, 27, 42, 27, 27, 27, 27, 42, 27, 27, 27, 27, 42, ...

If we only had enough time to take 5 massage time, then in statistical terms this means we have a sample size of 5 and in this case we use the standard deviation equation for a sample of a population:

s = √[∑ (x - M)^2/(N - 1)]


Where in, s is the standard deviation, x is each value in sample, M is the mean of the values, and N is the number of values (the sample size)

The rest of this work will be done in the case where we have a sample size of 5 massage time, therefore we will be using the standard deviation equation for a sample of a population.

Here are the 5 massage time

27, 27, 27, 27, 42

Now, let's calculate the standard deviation:

1. Calculate the mean:

(27 + 27 + 27 + 27 + 42)/5 = 30

2. Calculate x - M for each value in the sample:

27 - 30 = -3

27 - 30 = -3

27 - 30 = -3

27 - 30 = -3

42 - 30 = 12

3. Calculate ∑ (x - M)^2 = (-3)^2 + (-3)^2 + (-3)^2 + (-3)^2 + (12)^2 = 36 + 144 = 180.

4. Calculate the standard deviation,: s = √[∑ (x - M)^2/(N - 1)] = √[180/4)] = √45 = [spoiler]6.71[/spoiler] approx

barca14 wrote:A massage therapist provides sessions that last exactly 27 minutes, but as a reward to his customers, every fifth session is 42 minutes. If every customer comes for a very large number of sessions, what is the standard deviation of the massage time? Round your answer to three decimal places.

i got 6 as answer. reasoning
mean=(27*4+42*1)/5=30
30-27=3, 3^2=9
30-27=3 3^2=9
30-27=3 3^2=9
30-27=3 3^2=9
30-42=12 12^2=144

9*4+144*1=180
new mean=180/5=36-here my solving deviates with above solution as i divide new mean by 5 ( i saw the way gmat solves SD page 115 OG-12, theydivide by n , not by n-1)
SD=(36)^1/2=6

clock60 wrote:

barca14 wrote:A massage therapist provides sessions that last exactly 27 minutes, but as a reward to his customers, every fifth session is 42 minutes. If every customer comes for a very large number of sessions, what is the standard deviation of the massage time? Round your answer to three decimal places.

i got 6 as answer. reasoning
mean=(27*4+42*1)/5=30
30-27=3, 3^2=9
30-27=3 3^2=9
30-27=3 3^2=9
30-27=3 3^2=9
30-42=12 12^2=144

9*4+144*1=180
new mean=180/5=36-here my solving deviates with above solution as i divide new mean by 5 ( i saw the way gmat solves SD page 115 OG-12, theydivide by n , not by n-1)
SD=(36)^1/2=6

Please note that every customer comes for a very large number of sessions, and we are taking only a sample of it so it got to be divided by (N - 1) here.

And if they ask us to round our answer to three decimal places, then it would be [spoiler]6.708[/spoiler].

hi sanju09
do you mean that then the number of terms is limited. we must divide new mean by n.
and then the number of terms is great or infinite we must divide new mean by n-1?

clock60 wrote:hi sanju09
do you mean that then the number of terms is limited. we must divide new mean by n.
and then the number of terms is great or infinite we must divide new mean by n-1?

Whenever we consider a small sample of a considerably long list of data to find the SD from, the formula taken contains (N - 1) to its denominator. The illustration is too complicated and long, so just keep the gist of it.