Question

select the correct answer.
what is the shape of the following distribution?
{9, 10, 10, 11, 11, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 19, 20}
a. negative skew
b. positive skew
c. symmetric
d. asymmetric with no skew
e. none of the above

Explanation:

Step1: Calculate the median

The data set has 30 values. The median is the average of the 15th and 16th - ordered values. The 15th value is 15 and the 16th value is 15, so the median is $\frac{15 + 15}{2}=15$.

Step2: Calculate the mean

The sum of the data values: $9+2\times10 + 2\times11+2\times12+3\times13+4\times14+4\times15+4\times16+4\times17+18+19+20$
$=9 + 20+22+24+39+56+60+64+68+18+19+20$
$=419$.
The mean is $\frac{419}{30}\approx13.97$.

Step3: Analyze the skewness

Since the mean ($\approx13.97$) is less than the median (15), the distribution has a negative skew.

Answer:

A. negative skew