Question

(02.02 mc) arlo researched the starting salaries at the different companies that he applied to. here is the data he found: $35,850 $37,950 $34,830 $36,730 $35,920 $36,390 $36,730 $35,960 $35,920 $34,970 find the mean, median, and mode of the data set. show your work. edit view insert format tools table 12pt paragraph b i u a t²

Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$. First, sum up all the values:

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There are $n = 10$ data points. So the mean $\bar{x}=\frac{361250}{10}=36125$.

Step2: Find the median

First, order the data set: $34830,34970,35850,35920,35920,35960,36390,36730,36730,37950$.
Since $n = 10$ (even), the median is the average of the $\frac{n}{2}$-th and $(\frac{n}{2}+1)$-th values. The 5 - th value is $35920$ and the 6 - th value is $35960$. So the median $M=\frac{35920 + 35960}{2}=\frac{71880}{2}=35940$.

Step3: Determine the mode

The mode is the value that appears most frequently. In the data set, $35920$ and $36730$ each appear twice, and other values appear only once. So the modes are $35920$ and $36730$.

Answer:

The mean is $36125$, the median is $35940$, and the modes are $35920$ and $36730$.