Question

a meteorologist set up rain gauges at various locations around a city and recorded the rainfall amounts in the table below. use the data in the table to create a line plot using \\(\frac{1}{8}\\) inches.
a. which location received the most rainfall?
b. which location received the least rainfall?
c. which rainfall measurement was the most frequent?
d. what is the total rainfall in inches?

location	rainfall amount (inches)
2	\\(\frac{3}{8}\\)
3	\\(\frac{3}{4}\\)
4	\\(\frac{3}{4}\\)
5	\\(\frac{1}{4}\\)
6	\\(1\frac{1}{4}\\)
7	\\(\frac{1}{8}\\)
8	\\(\frac{1}{4}\\)
9	1
10	\\(\frac{1}{8}\\)

Explanation:

Part a

We compare the rainfall amounts for each location. The amounts are $\frac{1}{8}$, $\frac{3}{8}$, $\frac{3}{4}$, $\frac{3}{4}$, $\frac{1}{4}$, $1\frac{1}{4}$, $\frac{1}{8}$, $\frac{1}{4}$, $1$, $\frac{1}{8}$. Converting to eighths: $\frac{1}{8}$, $\frac{3}{8}$, $\frac{6}{8}$, $\frac{6}{8}$, $\frac{2}{8}$, $\frac{10}{8}$, $\frac{1}{8}$, $\frac{2}{8}$, $\frac{8}{8}$, $\frac{1}{8}$. The largest is $1\frac{1}{4}$ (location 6) and $1$ (location 9)? Wait, no, $1\frac{1}{4}=\frac{5}{4}=1.25$, $1 = 1$, so $1\frac{1}{4}$ is larger. Wait, wait, $1\frac{1}{4}$ is $1.25$, $1$ is $1$, $\frac{3}{4}=0.75$, so location 6 has $1\frac{1}{4}$ which is more than location 9's $1$. Wait, let's re - check the table: location 6 is $1\frac{1}{4}$, location 9 is $1$. So location 6 has the most.

We look at the smallest rainfall amounts. The amounts in eighths are $\frac{1}{8}$, $\frac{3}{8}$, $\frac{6}{8}$, $\frac{6}{8}$, $\frac{2}{8}$, $\frac{10}{8}$, $\frac{1}{8}$, $\frac{2}{8}$, $\frac{8}{8}$, $\frac{1}{8}$. The smallest is $\frac{1}{8}$, which occurs at locations 1, 7, 10.

We count the frequency of each rainfall amount. $\frac{1}{8}$: locations 1,7,10 (3 times); $\frac{3}{8}$: location 2 (1 time); $\frac{3}{4}$: locations 3,4 (2 times); $\frac{1}{4}$: locations 5,8 (2 times); $1\frac{1}{4}$: location 6 (1 time); $1$: location 9 (1 time). So $\frac{1}{8}$ has the highest frequency.

Answer:

Location 6

Part b