Question

the senior class at clearville isd is having a fundraiser to raise money for their prom. they are selling coupon books in the local community. the number currently sold by each of the students was used to create the box plot shown below. if one of the students calculated the mean of the data to be 14.5, would this be an appropriate mean?

○b. no, the mean should be higher.

○c. there is not enough information to determine if the mean is appropriate.

○d. no, the mean should be lower.

Explanation:

Step1: Analyze the box - plot data distribution

In a box - plot, the median is the middle value. Here, the data points (from left to right) are likely to be \(9\), \(16\), \(23\), \(28\), \(32\).

Step2: Calculate the mean

The formula for the mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). Here \(n = 5\), \(x_1=9\), \(x_2 = 16\), \(x_3=23\), \(x_4=28\), \(x_5=32\). Then \(\bar{x}=\frac{9 + 16+23+28+32}{5}=\frac{108}{5}=21.6\)

Since \(21.6>14.5\)

Answer:

B. No, the mean should be higher.