Question

salaries for the research and development department are given as $48,345, $27,982, $42,591, $19,522, $32,421, and $37,598. find the mean, the median, and the mode of the salaries.

1. the mean of the salaries is $34743.

(round to the nearest dollar as needed.)

1. the median is $

Explanation:

Step1: Arrange salaries in ascending order

$19522, 27982, 32421, 37598, 42591, 48345$

Step2: Calculate the mean

The mean formula is $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 6$ and $x_{i}$ are the individual salaries.
$\bar{x}=\frac{19522 + 27982+32421+37598+42591+48345}{6}=\frac{208459}{6}\approx34743.17\approx34743$

Step3: Calculate the median

Since $n = 6$ (an even - numbered data set), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. $\frac{n}{2}=3$ and $\frac{n}{2}+1 = 4$.
Median$=\frac{32421 + 37598}{2}=\frac{69919}{2}=34959.5\approx34960$

Step4: Check for mode

There is no repeated value in the data - set, so there is no mode.

Answer:

Mean: $\$34743$, Median: $\$34960$, Mode: None