What is the mean, variance, and standard deviation on cakes sold per day?

Question

What is the mean, variance, & standard deviation of the # of cakes sold per day. 12 cakes-probability .25; 13 cakes-probability .40; 14 cakes probability .25, & 15 cakes probability .10?

Answer 1

Dear Debra S,

For the mean, weight the outcomes by the probabilities and sum them:
mean = (0.25 x 12) + (0.40 x 13) + (0.25 x 14) + (0.10 x 15)
= 3.0 + 5.2 + 3.5 + 1.5
= 13.2 cakes per day.

For the variance, take the difference between each outcome and the mean, then square it. Then weight these quantities and sume them like you did when computing the mean:
variance = (0.25 x [12 - 13.2]^2) + (0.40 x [13 - 13.2]^2)
+ (0.25 x [14 - 13.2]^2) + (0.10 x [15 - 13.2]^2)
= (0.25 x [-1.2]^2) + (0.40 x [-0.2]^2) + (0.25 x [0.8]^2) + (0.10 x [1.8]^2)
= (0.25 x 1.44) + (0.40 x 0.04) + (0.25 x 0.64) + (0.10 x 3.24)
= 0.360 + 0.016 + 0.160 + 0.324
= 0.860 ("cakes per day" squared).

Once you have the variance, just calculate its square root to get the standard deviation:
standard deviation = variance^0.5
= 0.860^0.5
= 0.927 (cakes per day, to three decimal places).