Question

ms. herrera ran a sit - up competition among her p.e. students and monitored how many sit - ups each student could do.
sit - ups
7 7 124 124 124 124 124 198 198 198
x is the number of sit - ups that a randomly chosen student did. what is the expected value of x?
write your answer as a decimal.

Explanation:

Step1: Calculate total number of students

There are 2 students who did 7 sit - ups, 5 students who did 124 sit - ups and 3 students who did 198 sit - ups. So the total number of students $n=2 + 5+3=10$.

Step2: Calculate the sum of the products of each value and its frequency

The sum $S=(7\times2)+(124\times5)+(198\times3)$.
$7\times2 = 14$, $124\times5=620$, $198\times3 = 594$. Then $S=14 + 620+594=1228$.

Step3: Calculate the expected value

The expected value $E(X)=\frac{S}{n}$. Since $S = 1228$ and $n = 10$, $E(X)=\frac{1228}{10}=122.8$.

Answer:

$122.8$