Are the data Normal? Fruit fly thorax lengths. Here are the lengths in millimeters of the thorax for 49 male fruit flies:11 0.64 0.64 0.64 0.68 0.68 0.68 0.72 0.72 0.72 0.72 0.74 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.76 0.78 0.80 0.80 0.80 0.80 0.80 0.82 0.82 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.84 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.88 0.92 0.92 0.92 0.94

(a) Make a histogram of the distribution. Although the result depends a bit on your choice of classes, the distribution appears roughly symmetric with no outliers.

(b) Find the mean, median, standard deviation, and quartiles for these data. Comparing the mean and the median and comparing the distances of the two quartiles from the median suggest that the distribution is quite symmetric. Why?

(c) If the distribution were exactly Normal with the mean and standard deviation you found in (b), what proportion of observations would lie between the two quartiles you found in (b)? What proportion of the actual observations lie between the quartiles (include observations equal to either quartile value). Despite the discrepancy, this distribution is “close enough to Normal”for statistical work in later chapters.