Creek Ratz is a very popular restaurant located along the coast of northern Flor
ID: 2957473 • Letter: C
Question
Creek Ratz is a very popular restaurant located along the coast of northern Florida. They serve a variety of steak and seafood dinners. During the summer beach season, they do not take reservations or accept "call ahead" seating. Management of the restaurant is concerned with the time a patron must wait before being seated for dinner. Listed below is the wait time, in minutes, for the 25 tables seated last Saturday night.28 39 23 67 37 28 56 40 28 50
51 45 44 65 61 27 24 61 34 44
64 25 24 27 29 A A A A A
a. Explain why the times are a popuation.
b. find the mean and median of the times.
c. Find the range and the standard deviation of the times.
Explanation / Answer
(a) A statistical population:
This is a set upon which statistical information or inferences can be deducted. In this case we have a random sample from the “wait times” population. Among the general concept or population of “wait times” we are looking at the specific wait times for this restaurant for a specific meal. It is therefore a well defined set of entities or a population. The 25 occurrences noted or measured on that day are a sample on which we can through statistical analysis draw general conclusions, which is what we are about to do in the next answers (b and c).
(b) Mean and median:
Placed in increasing order the 25 observations are:
23
24
24
25
27
27
28
28
28
29
34
37
39
40
44
44
45
50
51
56
61
61
64
65
67
There are 25 elements and the total is: 1021
The average or mean will be total divided by 25: 40.84 or 40 minutes and 50.4 seconds
The mifdde number in the ordered list is the 13th or 39, so the median is 39.
(c) Range and standard deviation:
The range is simply the difference bet ween the largest (67) and smallest (23) observation so:
R = 67-23 = 44
The standard deviation is the square root of the variance, and the variance is the average of the differences between the observations and the mean, squared to make them all positive.
If x1,x2,x3 are the observations, and m the mean, the varaiance is the average of the (xi-m)2
So:
V = [ sum (xi – m)2 ] / 25
And standard deviation S :
S = V (that is square root of V)
S = { [sum (xi – m)2 ] / 25 } (that is square root of {...}
The table below show the Xi, the (xi-m)2 and the total of both lists.
Below the totals the mean (Total/25) and the variance (Total-V/25) and the standard deviation which is the square root of the variance.
xi
(xi-m)2
23
318.2656
24
283.5856
24
283.5856
25
250.9056
27
191.5456
27
191.5456
28
164.8656
28
164.8656
28
164.8656
29
140.1856
34
46.7856
37
14.7456
39
3.3856
40
0.7056
44
9.9856
44
9.9856
45
17.3056
50
83.9056
51
103.2256
56
229.8256
61
406.4256
61
406.4256
64
536.3856
65
583.7056
67
684.3456
Total:
Total
1021
5291.36
Mean:
Variance:
211.6544
St. dev:
14.54835
23
24
24
25
27
27
28
28
28
29
34
37
39
40
44
44
45
50
51
56
61
61
64
65
67
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