Question

A pottery factory kept track of the number of broken plates per shipment Number of broken plates Number of shipments 2 376 2 380 6 567 5 737 2 928 964 3 X is the number of broken plates that a randomly chosen shipment had. What is the expected value of X? Write your answer as a decimal.

Answer 1

Answer: The expected value of X is 672.75

Expected value can be calculated using the below formula

`\begin{gathered} \text{Expected value = }(\Sigma fx)/(\Sigma f) \\ \Sigma fx\text{ = 376 x 2 + 380 x 2 + 567 x 6 + 737 x 5 + 928 x 2 + 964 x 3} \\ \Sigma fx\text{ = 752 + 760 + 3, 402 + 3, 685 + 1, 964 + 2, 892} \\ \Sigma fx\text{ = 13, 455} \\ \Sigma f\text{ = 2 + 2 + 6 + 5 + 2 + 3} \\ \Sigma f\text{ = 20} \\ \text{Expected value = }\frac{13,\text{ 455}}{20} \\ \text{Expected value = 672.75} \end{gathered}`

Therefore, the expected value of X is 672.75