Question

for the following situation, find the mean and standard deviation of the population. list all samples (with replacement) of the given size from that population and find the mean of each. find the mean and standard deviation of the sampling distribution and compare them with the mean and standard deviation of the population. the word counts of five essays are 508, 639, 552, 612, and 575. use a sample size of 2. the mean of the population is (round to two decimal places as needed.)

Explanation:

Step1: Recall mean formula

The mean of a population $\mu=\frac{\sum_{i = 1}^{N}x_{i}}{N}$, where $x_{i}$ are the data - points and $N$ is the number of data - points. Here, $N = 5$, $x_1=508$, $x_2 = 639$, $x_3=552$, $x_4=612$, $x_5=575$.
$\mu=\frac{508 + 639+552+612+575}{5}$

Step2: Calculate the sum in the numerator

$508+639+552+612+575=(508+639)+(552+612)+575 = 1147+1164+575=2886$

Step3: Calculate the mean

$\mu=\frac{2886}{5}=577.20$

Answer:

$577.20$