Describe the distribution of heights such as center, unusual features, shape, spread.

Question

63 64 61 65 63 67 68 62 73 70 66 72 62 63 62 68 66 67 72 72 66 60 64.8 62 62 63 68

Answer 1

This is a question that involves summary measures. To describe the distribution of your data, you'll want to generally plot the data first to check what kind of measure of central tendency you want to use. In your case, when we plot your data using a density plot (just finding out where the data points are in a density curve), we can see that the data is more concentrated on the left but not by too much, so we can still use the arithmetic mean (average) to describe the data.

CENTER:

We can use the mean to describe the center by just taking the average of all the data (so, add everything together and divide by 27 (number of data points). Another measure for central tendency can be the median, which you can find by sorting the list of data points from smallest to greatest and finding the middle of the dataset. Since you have an odd (27) number of data points, the median will be the 14th data point after sorting the data. Lastly, we typically also report the mode, which is the data value that appears the most.

So, for describing the center, you'll want to report the mean, median, and mode.

UNUSUAL FEATURES:

Look at the density plot, what do you notice? We see that the data is slightly more concentrated on the left but still fairly normal (curve still looks like a bell curve). You can probably describe exactly what I said about some more data on the left, a little bit of right skew, but overall fairly normal.

SHAPE:

See above.

SPREAD:

Measures of spread include measures like range (difference between maximum and minimum), interquartile range (difference between the 75% percentile and 25% percentile of the data), standard deviation, and variance (square of the standard deviation).

Overall, this should be a fairly thorough answer to guide you on which summary statistics to report!