Question

Country music The lengths, in minutes, of the 50 most popular mp3 downloads of songs by country artist Dierks Bentley are given here.

Make a histogram to display the data. Write a few sentences describing the distribution of song lengths.

Short answer

Rightward skewed

Two possible outliers

The median time is approximately 3.75 minutes.

The song lengths appear to range between 29 and 7 minutes.

Step-by-step solution

Given information. 

Step 2. Create a histogram to represent the data.

Table of frequencies

First, we'll calculate the frequency of each interval, which is the number of data values that fall within each interval. The first interval is 2.5-<3 because it begins at 2.5 and has a width of 0.5. The next intervals will be 3-<3.5, 3.5-<4, and so on until all data values are assigned to exactly one interval.

The frequency is then defined as the number of data values that belong to the class.

Histogram of Frequency

Each bar must have the same width and be bounded by the interval boundaries, while the height must be equal to the frequency.

Because the highest bars are to the left in the histogram, with a tail of smaller bars to the right, the distribution is skewed to the right.

Because there are two bars (with frequency 1) that are separated from the rest of the histogram by a gap, the distribution appears to have two outliers.

The median is the value in the middle of the distribution. The median length of the songs appears to be around 3.75 minutes (which is the middle of the highest bar).

The song lengths appear to range between 2.9 and 7 minutes.

As a results:

Rightward skewed

Two possible outliers

The median time is approximately 3.75 minutes.

The song lengths appear to range between 29 and 7 minutes.