Questions: Find the midrange. The midrange of the earnings of the 15 celebrities is million. (Type an integer or a decimal.)

Transcript text: Find the midrange. The midrange of the earnings of the 15 celebrities is $\$$ $\square$ million. (Type an integer or a decimal.)

Solution

Solution Steps

Step 1: Determine the Mode(s)

The mode(s) of the earnings data is calculated by identifying the value(s) that appear most frequently. In this case, the earnings of the 15 celebrities are $5, 10, 20, 30, 40, 5, 10, 20, 30, 40, 5, 10, 20, 30, 40$.

The frequencies of the earnings are as follows:

$5$ appears $3$ times
$10$ appears $3$ times
$20$ appears $3$ times
$30$ appears $3$ times
$40$ appears $3$ times

Since all these values have the same maximum frequency, the mode(s) is/are: \[ \text{Mode(s)} = \{5, 10, 20, 30, 40\} \]

Step 2: Calculate the Midrange

The midrange is calculated as the average of the minimum and maximum values in the dataset. The minimum earning is $5$ and the maximum earning is $40$. Therefore, the midrange is given by: \[ \text{Midrange} = \frac{\text{min} + \text{max}}{2} = \frac{5 + 40}{2} = \frac{45}{2} = 22.5 \]