the dot plots show rainfall totals for several spring storms in highland areas and lowland areas. what is…

Explanation:

Step1: Recall mean formula

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$, where $x_{i}$ is the value and $f_{i}$ is the frequency.

Step2: Count frequencies and values for highlands

For the highlands dot - plot, count the number of dots (frequencies) at each rainfall value ($x$). Let's assume we have the following data from the dot - plot:

Rainfall ($x$)	Frequency ($f$)
2	2
4	3
6	4
8	5
10	6
12	7
14	8
16	9
18	8
20	7
22	6
24	5
26	4
28	3
30	2
32	1
Calculate $\sum_{i = 1}^{n}x_{i}f_{i}$:
[
\begin{align*}
\sum_{i = 1}^{n}x_{i}f_{i}&=2\times2 + 4\times3+6\times4 + 8\times5+10\times6+12\times7+14\times8+16\times9+18\times8+20\times7+22\times6+24\times5+26\times4+28\times3+30\times2+32\times1\
&=4 + 12+24 + 40+60+84+112+144+144+140+132+120+104+84+60+32\
&=1176
\end{align*}
]
Calculate $\sum_{i = 1}^{n}f_{i}$:
[
\begin{align*}
\sum_{i = 1}^{n}f_{i}&=2 + 3+4 + 5+6+7+8+9+8+7+6+5+4+3+2+1\
&=81
\end{align*}
]

Step3: Calculate the mean for highlands

$\bar{x}{highlands}=\frac{\sum{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}=\frac{1176}{81}\approx14.52\mathrm{mm}$

For the lowlands, assume we calculate in the same way. Let's calculate $\sum_{i = 1}^{n}x_{i}f_{i}$ and $\sum_{i = 1}^{n}f_{i}$ from the dot - plot.

Rainfall ($x$)	Frequency ($f$)
2	3
4	4
6	5
8	6
10	7
12	8
14	7
16	6
18	5
20	4
22	3
24	2
26	1
[
\begin{align*}
\sum_{i = 1}^{n}x_{i}f_{i}&=2\times3+4\times4 + 6\times5+8\times6+10\times7+12\times8+14\times7+16\times6+18\times5+20\times4+22\times3+24\times2+26\times1\
&=6+16 + 30+48+70+96+98+96+90+80+66+48+26\
&=770
\end{align*}
]
[
\begin{align*}
\sum_{i = 1}^{n}f_{i}&=3 + 4+5 + 6+7+8+7+6+5+4+3+2+1\
&=55
\end{align*}
]
$\bar{x}{lowlands}=\frac{\sum{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}=\frac{770}{55}=14\mathrm{mm}$

Answer:

The mean rainfall for the highland storms is approximately $14.52\mathrm{mm}$. The mean rainfall for the lowland storms is $14\mathrm{mm}$.