Question

a sociologist looks at trends in flea - borne typhus cases among humans in a certain county. flea - borne typhus, human cases by year for the entire county, years 1–20 *at year 20, the current 5 - year average was 99.6 cases per year, based on the data from years 16–20. adapted from http://publichealth.lacounty.gov/ at year 14, which of the following would be the most likely current 5 - year average? a. 38.0 b. 50.6 c. 64.2 d. 74.0

Explanation:

Step1: Identify data for years 10 - 14

From the graph, the number of cases for years 10, 11, 12, 13, 14 are 38, 49, 68, 44, 54 respectively.

Step2: Calculate the 5 - year average

The formula for the average of \(n\) numbers \(x_1,x_2,\cdots,x_n\) is \(\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}\). Here \(n = 5\), \(x_1=38\), \(x_2 = 49\), \(x_3=68\), \(x_4 = 44\), \(x_5=54\).
First, find the sum: \(38 + 49+68 + 44+54=38+49 = 87\); \(87+68 = 155\); \(155 + 44=199\); \(199+54 = 253\).
Then, the average is \(\frac{253}{5}=50.6\).

Answer:

B. 50.6