Question

(1 point)
some students conducted a survey on some people’s weekly income:
$137200, $800, $1700, $1800, $1800, $1300
the mean of these people’s weekly income is 21400
the median of these people’s weekly income is 1750
include $ in your answer.
which number, mean or median, is a better way to represent these people’s weekly income?
○ mean
● median
note: you can earn partial credit on this problem.
you are in the reduced scoring period: all additional work done counts 85% of the original.
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Explanation:

For Mean Calculation:

Step1: Sum all incomes

To find the mean, we first sum all the weekly incomes. The incomes are $\$137200$, $\$800$, $\$1700$, $\$1800$, $\$1800$, $\$1300$. So the sum $S = 137200 + 800 + 1700 + 1800 + 1800 + 1300$.
Calculating the sum: $137200+800 = 138000$; $138000 + 1700 = 139700$; $139700+1800 = 141500$; $141500 + 1800 = 143300$; $143300+1300 = 144600$.

Step2: Divide by number of data points

There are 6 data points. The mean $\bar{x}=\frac{S}{n}$, where $n = 6$ and $S=144600$. So $\bar{x}=\frac{144600}{6}=24100$? Wait, the given mean in the problem was 21400, maybe I miscalculated. Wait, let's recalculate the sum: $137200+800 = 138000$; $138000+1700 = 139700$; $139700+1800 = 141500$; $141500+1800 = 143300$; $143300+1300 = 144600$. Then $\frac{144600}{6}=24100$. But the problem had 21400, maybe a typo, but let's proceed with the correct calculation.
Wait, maybe the original problem had a different set, but assuming we follow the correct method.

Step3: Mean formula

The formula for the mean (average) is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $x_{i}$ are the data points and $n$ is the number of data points.

For Median Calculation:

Step1: Order the data

To find the median, we first order the data from smallest to largest. The incomes are: $\$800$, $\$1300$, $\$1700$, $\$1800$, $\$1800$, $\$137200$.

Step2: Find the middle value(s)

Since there are 6 (even number) data points, the median is the average of the 3rd and 4th values. The 3rd value is $\$1700$ and the 4th value is $\$1800$. So median $=\frac{1700 + 1800}{2}=\frac{3500}{2}=1750$, which matches the given median.

For choosing between mean and median:

The mean is affected by extreme values (like $\$137200$ here, which is much larger than the other incomes). The median is resistant to outliers. Since there is an outlier (the very high income of $\$137200$) that skews the mean, the median better represents the typical weekly income of most people (as most incomes are much lower than the mean due to the outlier).

Answer:

For mean (correct calculation): $\$24100$ (if we calculate correctly, but the problem's given mean might have an error). For median: $\$1750$. And the better representation is median.