Please help me in answering the following statistic problems. I am
reviewing for an exam -- Thanks!

37. Anderson, Inc., is a distributor of small electrical motors. As
with any business, the length of time customers take to pay their
invoices is important. Listed below, arranged from smallest to
largest, is the time, in days, for a sample of Anderson,
Inc., invoices.

13 13 13 20 26 27 31 34 34 34 35 35 36 37 38
41 41 41 45 47 47 47 50 51 53 54 56 62 67 82

a. Determine the first and third quartiles.
b. Determine the 2nd decile and the 8th decile.
c. Determine the 67th percentile.


38. Wendy Hagel is the national sales manager for National Textbooks,
Inc. She has a sales
staff of 40 who visit college professors all over the United States.
Each Saturday morning
she requires her sales staff to send her a report. This report
includes, among other things,
the number of professors visited during the previous week. Listed
below, ordered from
smallest to largest, are the number of visits last week.

38 40 41 45 48 48 50 50 51 51 52 52 53 54 55 55 55 56 56 57
59 59 59 62 62 62 63 64 65 66 66 67 67 69 69 71 77 78 79 79

a. Determine the median number of calls.
b. Determine the first and third quartiles.
c. Determine the 1st decile and the 9th decile.
d. Determine the 33rd percentile.


55. The ages of a sample of Canadian tourists flying from Toronto to
Hong Kong were: 32, 21,
60, 47, 54, 17, 72, 55, 33, and 41.
a. Compute the range.
b. Compute the mean deviation.
c. Compute the standard deviation.

Hi mrynot!
Here are the answers to your questions.

Question 1

At the following link you can find a definition of the quantiles
(quartiles, deciles, percentiles) and how to calculate them:

Quantile
http://encyclopedia.thefreedictionary.com/quantile

Esentially, the quartiles are the three data points in a sample that
divide the sample into four equal-sized sub-samples; the deciles are
the nine points that divide a sample in ten; and the percentiles are
the 99 points that divide a sample in 100. Of course, approximations
need to be done, because samples can't always be divided in exactly
equal-sized 4, 10 or 100 sub-samples.

Using the methodology explained in the link, we get that:

First Quartile:  34
Third Quartile:  50
Second Decile:   29
Eighth Decile:   52
67th Percentile: 47


Question 2

We use exactly the same methodology as in the previous question,
recalling the the "median" is the value that divides the sample in two
equal-sized groups.

Median:          58
1st Quartile:    51.5
3rd Quartile:    66
1st Decile:      46.5
9th Decile:      74
33rd Percentile: 54


Question 3

For this question, please check the following link, which explains the
deifinitions of range, mean deviation, standard deviation, and how to
calculate each of them:

Measures Of Variability
http://www.math.bcit.ca/faculty/david_sabo/apples/math2441/section3/variability/variability.htm

a. The range is simply the largest value minus the smallest value of a
sample. In this case:

Range = 72-17 = 55

b. In order to calculate the mean deviation and the standard
deviation, we must find the mean of this sample. This is:

32+21+60+47+54+17+72+55+33+41
----------------------------- = 43.2
            10

Therefore, using the formula in the link, the mean deviation is:

 |32-43.2| + |21-43.2| + |60-43.2| + ... + |41-43.2|
---------------------------------------------------- =
                       10

 11.2      +   22.2    + 16.8    +  ...  +    2.2
---------------------------------------------------- = 14.4
                       10

So the mean deviation is 14.4

c. Finally, the sample variance is:

(32.2-43.2)^2 + (21-43.2)^2 + ... + (41-43.2)^2
----------------------------------------------- = 310.62
                     9

So the sample standard deviation is the square root of this number, that is, 17.62.


Google search terms
quantiles statistics definition
://www.google.com/search?q=quantiles+statistics+definition&hl=en&lr=&start=20&sa=N
statistics range "standard deviation"
://www.google.com/search?hl=en&q=statistics+range+%22standard+deviation%22


I hope this helps! If you have any questions regarding my answer,
please don't hesitate to request a clarification. Otherwise I await
your rating and final comments.

Best wishes!
elmarto

Thank you for your assistance; much appreciated. I do have 3 other
questions that need addressed in this same category (statistics) -- I
am not sure how to point you to those too, but if you would like to
tackle those it would be very helpful.

Thanks!