Answer
We conclude that the data set is normal. Please see explanations below.
Work Step by Step
1. We first construct a frequency table and make a histogram as shown in the figure.
It appears that the distribution is right skewed.
2. We use Pearson Coefficient to test for skewness. We can obtain the mean $\bar X=147.04$,
median=$138.5$, and standard deviation $s=93.5$ so
$PC=\frac{3(147.04-138.5)}{93.5}=0.274$ which does not indicate strong skewness.
3. We identify outliers. With $IQR=138$ the range to test outliers can be set up as
$147.04-1.5\times138=-60$ to $147.04+1.5\times138=354.04$ and we can find one outlier as 435.
Conclusion, although the histogram does not show a bell-shaped curve, Pearson Coefficient does
not indicate strong skewness, and the outlier test find only one outlier out of 50 points.
We conclude that the data set is normal.
