The following frequency table summarizes a set of data. Value Frequency
2 3
3 2
5 1
6 3
7 1
8 2
11 3

For the above data set, you are interested to determine the "spread" of the data.

Would you employ calculations for the sample standard deviation, or population standard deviation for this data set?
You are interested in the heights of students at a particular middle school. Your data set represents the heights of all students in the middle school with 600 students.

Select the correct answer below:

a. Use calculations for sample standard deviation.
b. Use calculations for population standard deviation.

Part A

The population standard deviation is suitable for this dataset as it isnt given whether its a sample or a population distribution and it sure doesn't seem like the findings from such a dataset is to be generalized for some population distribution.

Part B

This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.

Step-by-step explanation:

The spread of a dataset is usually the measure of dispersion, a measure of the way the distribution spreads out from a particular mean value.

The problem of which type of standard deviation one should calculate usually arises a lot in Statistics. As the name sounds, population standard deviation usually uses all of the distribution to compute while the sample standard deviation uses the data from the sample distribution

The best advice on when to use the population stamdard deviation formula is that

(1) we have the entire population or

(2) we have a sample of a larger population, but we are only interested in this sample and do not wish to generalize the statistical findings to the population.

The sample standard deviation formula is used when one has a sample of a larger population, one is not only interested in this sample and one wishes to generalize the findings to the population.

The population standard deviation is given as

σ = √[Σ(x - xbar)²/N]

Sample standard deviation

σ = √{[Σ(x - xbar)²]/N-1)}

The only difference is the N and (N-1).

So, for the questions presented,

Part A.

Here, it is evident that the findings for this dataset in the question is just for this dataset, hence,the population standard deviation is suitable for this dataset.

Part B

This is outrightly a population distribution of all the students in the middle school, So, the spread of the height of all students about a mean is best indicated using the population standard deviation.

Hope this Helps!!!

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