Question

simons p.e. class participated in a push - up competition, and simon wrote down how many push - ups each person could do. push - ups 0 0 0 0 0 23 23 23 23 23 50 50 50 50 73 73 73 92 92 92 x is the number of push - ups that a randomly chosen person did. what is the expected value of x? write your answer as a decimal.

Explanation:

Step1: Count the frequency of each value

There are 5 zeros, 5 twenty - threes, 4 fifties, 3 seventies - threes, 4 nineties - twos. The total number of data points is $5 + 5+4 + 3+4=21$.

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

The sum is $0\times5+23\times5 + 50\times4+73\times3+92\times4=0 + 115+200+219+368 = 902$.

Step3: Calculate the expected value

The expected value $E(X)=\frac{902}{21}\approx42.952381$. Rounding to two decimal places, we get $42.95$.

Answer:

$42.95$