Would u all help me to answer this ?

Question

The manager of a fast-food restaurant selected several cash register receipts at random. The amounts spent by customers were $12, $15, $16, $10, and $27. Compute the: a. range b. the mean c. the sample variance d. the sample standard deviation

Please help to answer this. I really have no idea about it. This question is rather easy for u all. I will provide BA.

Answer 1

the sample standard deviation would be 6.595

You have to minus 1 from the N, 174/(5-1)=43.5

Sqrt 43.5=6.595

Answer 2

Range: 15

Mean: 16

I don't know the others. What math class is this?

Answer 3

A: The Range is the length of the smallest interval which contains all the data. It is calculated by subtracting the smallest observations from the greatest.

27 - 10 = 17

B: the mean of a list of numbers is the sum of all the members of the list divided by the number of items in the list

12 + 15 + 16 + 10 + 27 = 80

80 / 5 = 16

C: The variance is equal to the mean of the squares minus the square of the mean

Mean of the squares =

[(12*12) + (15*15) + (16*16) + (10*10) + (27*27)] / 5

[144 + 225 + 256 + 100 + 729] / 5

[1454] / 5 = 290.80

Square of the mean=

(16*16) = 256

So the variance would be=

290.80 - 256 = 34.80

D: To compute the standard deviation of the set first find the mean, then find the individual deviations from the mean. Square the individual deviations and add them together. Divide the result by the number of members of the set. Take the square root and round to two decimal places.

Remember the mean = 16.

Individual deviations from the mean (the numbers have to be positive, so always put the higher number first)=

16 - 12 = 4

16 - 15 = 1

16 - 16 = 0

16 - 10 = 6

27 - 16 = 11

Square the individual deviations and add them together=

(4*4) + (1*1) + (0*0) + (6*6) + (11*11) =

16 + 1 + 0 + 36 + 121 = 174

Divide the result by the members of the set=

174 / 5 = 34.80

Take the square root and round to two decimal places=

sqrt 34.80 = 5.90

So A = 17 ; B = 16 ; C = 34.80 ; D = 5.90

I hope that helps. I know it's a lot of info put into this little box, but I hope I explained it in such a way you could figure it out.

Good luck.

Additional: Oh and btw, ruckason's answer for range is incorrect, what he gave you is the median, not the range. The median is the number separating the higher half of a sample  from the lower half. Just thought I would clarify that so you didn't get confused.