What is the expected height (in inches)?

Question

Heights (in inches) obtained by a group of people in a random survey are reported in the following table:

Height	Probability
55	0.01
60	0.026
65	0.132
70	0.332
75	0.332
80	0.132
85	0.026
90	0.01

What is the expected height (in inches)?

Answer 1

I'm going to assume the height is not a range but exact values (in other words that there is nobody with a height of 56 inches) - which seems a bit weird. It seems like the table should be listing ranges (small to large). If so, the answer would be different.

Expected value = x₁P₁ + x₂P₂ + x₃P₃ + . . . x_nP_n

So the expected height (EH) is found by multiplying height by probability and adding them all up:

EH = h₁P(h₁) + h₂P(h₂) + h₃P(h₃) +h₄P(h₄) + h₅P(h₅) + h₆P(h₆) + h₇P(h₇) + h₈P(h₈)

EH = 55(0.01) + 60(0.026) + 65(0.132) + 70(0.332) + 75(0.332) + 80(0.132) + 85(0.026) + 90(0.01)

EH = 72.5 inches

Answer 2

To find the expected value for this problem, you would have to multiply each probability times its respective height value and all those up,, i.e. 55*.01+60*0.026+65*.132+70*.332......