Question

Most dermatologists recommend using sunscreens that have a sun protection factor ( SPF) of at least 30. One professor wanted to find out whether the SPF of sunscreens used by students at the professor's school (which is in a very sunny part of the United States) exceeds this value, on average. To collect data, the professor surveyed students in an Introductory Statistics course and found that in a sample of 48 students, the mean SPF was 35.29 Select the graph type(s) that could be used to visualize the variable SPF of sunscreen used. Select the statistics that can be used to describe the variable SPF of sunscreen used. Select all that apply. The mean SPF of sunscreen used, The standard deviation of SPF of sunscreen used, The median SPF of sunscreen used, The proportion of sunscreens used with SPF more than 30, The number of sunscreens used with SPF more than 30

Answer 1

To visualize the variable SPF of sunscreen used, suitable graph types include:

1. Histogram: This graph can show the distribution of SPF values among the students.
2. Boxplot: This can visually summarize the median, quartiles, and potential outliers in the SPF data.
3. Dot Plot: This can provide a clear view of all the individual SPF values and their frequencies.

For describing the variable SPF of sunscreen used, the following statistics can be applied:

1. The mean SPF of sunscreen used: This provides the average SPF.
2. The standard deviation of SPF of sunscreen used: This indicates how much variation exists from the mean.
3. The median SPF of sunscreen used: This gives the middle value of the data set, which is useful for understanding the central tendency, particularly if there are outliers.
4. The proportion of sunscreens used with SPF more than 30: This shows the relative frequency of sunscreens exceeding the recommended SPF.
5. The number of sunscreens used with SPF more than 30: This provides a count of how many students used sunscreens with SPF above 30.

In conclusion, all the selected statistics can be used to describe the SPF data effectively.