#3- Comparing Sample and Population Descriptive Statistics

In summary, with both variables (Current Value and Operating Income), the population dataset had a larger

standard deviation, mean and positive skewness than the sample dataset, as broken down specifically

underneath their charts. Both samples also had a lower coefficient of variation than the populations, showing

that the standard deviation decreased to a higher proportion than the mean decreased. However, the quartile

values and interquartile ranges stayed relatively similar.

This can be explained by the removal of outliers and extreme values from the dataset when random samples are

taken. One, respectively two, values of each variable were abnormally high and caused the standard deviation,

mean and positive skewness to increase by its existence, leaving, however, the quartiles and median rather

unchanged. Since a random sample was taken, these values were left out of the random sample, so the increases

of values they would have carried out did not take place- hence, the decrease in them. This can be attributed to a

phenomenon called the Central Limit Theorem, where a large enough sample can get closer to a normal

distribution even if the population is skewed, and we can see that while not perfectly normal, taking a sample

does cause the dataset to have a more normal distribution than before.

#4- Calculating Confidence Intervals

We will assume a 95% confidence interval for Current Value and Operating Income, meaning 95% of the time,

the mean values of both will fall within the range we calculate. We are calculating from the samples, not

populations, so since there are 11 pieces of data (less than 30), we will use a t-table.

T (a/2) = t0.025, at 10 degrees of freedom (n-1) = 2.228

Current Value- mean = 1820.9091, standard deviation = 503.15911, n = 11

 2.228*(503.15911/sqrt(11)) = 338.006

 Interval at 95% = 1820.9091 +- 338.006

 Real population mean = 1965.9375. It is contained within the estimate.

Operating Income- mean = 67.1636, standard deviation = 31.44930, n = 11

 2.228*(31.44930/sqrt(11)) = 21.136

 Interval at 95% = 67.1636 +- 21.136

 Real population mean = 76.2125. It is contained within the estimate.

Since the findings of the sample showed that 95% of the time, the mean would be within the given interval, it

was expected that both population means would fall within this range, which they did. This indicates that it was

possible to accurately infer a range for the mean from the population based upon that of the sample.

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