Question

Bed day offers savings of $10, $25, $50 and $100 off on their already low price on bedroom suites. Select a coupon and save the amount on the coupon. There are a total of 100 coupons with 70, 20, 8 and 2 containing $10, $25, $50, and $100, respectively. I figured out that the average saving is $46.25. Am I right? Determine the standard deviation.
A. $39.45
B. $34.16
C. $16.55
D. $16.46

Answer 1

Unfortunately, you calculated the mean incorrectly. To calculate the mean, you multiply the value of each coupon by the number of coupons with that value.

For example, for the 10 dollar coupon, you multiply 10 times 70. So you get 700 for that coupon. For the 25 dollar coupon, you multiple 25 times 20. You get 500 for that coupon. You do the same thing for the other two coupons.

So you have:
10x70=700
25x20=500
50x8=400
100x2=200

Next add the totals for each coupon value.

So you have 700+500+400+200=1800

Next divide the total value by the number of coupons.

So you have 1800/100=18

So your mean is $18

Answer 2

To calculate the standard deviation, first you subtract the mean value from the coupon value and square it.

So for the 10 dollar coupon you would have this:

10-18=-8 Now square it. So we have this:
(-8)^2=64

For the rest of the coupons we have this:

25-18=7
7^2=49

50-18=32
32^2=1024

100-18=82
82^2=6724

Next multiply each squared value by the number of coupons with that value. So we would have this for the 10 dollar coupon.

70x64=4480

Do the same thing for the other coupons.

20x49=980
8x1024=8192
2x6724=13448

Next add up the four totals. So we have this:

4480+980+8192+13448=27100

Next divide this total by the number of coupons. So we have this:

27100/100=271

Finally, take the square root of the number just calculated. So we have this:

sqrt(271)=16.46

So 16.46 is the standard deviation.