What is the sample mean for the data?

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1 Answer
May 23, 2018

The sample mean of the last 10 data points is #barx = 8.4#.


It is unclear from the wording of the question, but since the second data set contains only 10 data points out of a possible 24, I am assuming these 10 members is what we're calling our "sample".

Under this assumption, the sample mean for these 10 data is

#barx = (8+8+8.5+8+9+8+9+9+8.5+8)/10#
#color(white)barx = 84/10#

#color(white)barx = 8.4#


While these 10 members are a sample from a population, they are not a sample from the first set of 24 data points. This is because the second set of measurements was taken on a different night, and so the hours of sleep for each member might have changed.

If we treat the #24+10 = 34 # data points as a sample from a worldwide population of "hours of sleep the night before a musical", then we'd get a sample mean of

#barx = (8+8.5+8+7.5+...+9 + 8.5 + 8)/34#
#color(white)barx = 275.5/34#

#color(white)barx ~~ 8.10#

It all depends on which population we're trying to estimate the mean from.