Mr. Hamilton is placing a support plank along the diagonal of a gate. The height of the gate is 5 feet, and the diagonal is 1 foot longer than the width of the gate, as shown below.

132.5

Step-by-step explanation:

First, find the mean of the numbers given.  To calculate the mean, or average of any number set, add up all the numbers in the set and then divide that sum by the number of numbers in the set.

The mean of this given data is:

add up all the numbers: 147+141+120+124+128=660

there are 5 numbers in the set, so divide the sum by 5: 660/5=132

The next step in finding the difference is to subtract the mean from each number and square each resulting difference.

147-132=15^2=225

141-132=9^2=81

120-132=(-12)^2=144

124-132=(-8)^2=64

128-132=(-4)^2=16

Finally, find the mean, or average, of the squared difference.

add them all up: 225+81+144+64+16=530

the only difference with the division is that the divisor is the number of numbers minus 1, so in this case 5-1, which equals 4

so, now divide: 530/4=132.5

So, the variance of the given data is 132.5