Question

The American Society of PeriAnesthesia Nurses (ASPAN; www.aspan.org) is a national organization serving nurses practicing in ambulatory surgery, preanesthesia, and postanesthesia care. The organization's membership is listed below.

State/Region	Membership
Alabama		138
Arizona		489
Maryland, Delaware, DC		551
Connecticut		273
Florida		522
Georgia		461
Hawaii		87
Maine		145
Minnesota, Dakotas		385
Missouri, Kansas		194
Mississippi		87
Nebraska		73
North Carolina		387
Nevada		64
New Jersey, Bermuda		531
Alaska, Idaho, Montana,Oregon, Washington		640
New York		966
Ohio		888
Oklahoma		164
Arkansas		93
Illinois		498
Indiana		362
Iowa		128
Kentucky		205
Louisiana		158
Michigan		467
Massachusetts		341
California		1,098
New Mexico		37
Pennsylvania		371
Rhode Island		65
Colorado		247
South Carolina		284
Texas		1,108
Tennessee		219
Utah		87
Virginia		353
Vermont, New Hampshire		134
Wisconsin		257
West Virginia		60

find standard deviation, first and third quartile, and the limits for the outliers

Answer 1

To find Standard deviation we need to find mean first

Create the following table.

data	data-mean	(data - mean)2
138	-202.425	40975.880625
489	148.575	22074.530625
551	210.575	44341.830625
273	-67.425	4546.130625
522	181.575	32969.480625
461	120.575	14538.330625
87	-253.425	64224.230625
145	-195.425	38190.930625
385	44.575	1986.930625
194	-146.425	21440.280625
87	-253.425	64224.230625
73	-267.425	71516.130625
387	46.575	2169.230625
64	-276.425	76410.780625
531	190.575	36318.830625
640	299.575	89745.180625
966	625.575	391344.080625
888	547.575	299838.380625
164	-176.425	31125.780625
93	-247.425	61219.130625
498	157.575	24829.880625
362	21.575	465.480625
128	-212.425	45124.380625
205	-135.425	18339.930625
158	-182.425	33278.880625
467	126.575	16021.230625
341	0.57499999999999	0.33062499999999
1098	757.575	573919.880625
37	-303.425	92066.730625
371	30.575	934.830625
65	-275.425	75858.930625
247	-93.425	8728.230625
284	-56.425	3183.780625
1108	767.575	589171.380625
219	-121.425	14744.030625
87	-253.425	64224.230625
353	12.575	158.130625
134	-206.425	42611.280625
257	-83.425	6959.730625
60	-280.425	78638.180625

Find the sum of numbers in the last column to get.

So standard deviation =

The first quartile (or lower quartile or 25th percentile) is the median of the bottom half of the numbers. So, to find the first quartile, we need to place the numbers in value order and find the bottom half.

37   60   64   65   73   87   87   87   93   128   134   138   145   158   164   194   205   219   247   257   273   284   341   353   362   371   385   387   461   467   489   498   522   531   551   640   888   966   1098   1108   

So, the bottom half is

37   60   64   65   73   87   87   87   93   128   134   138   145   158   164   194   205   219   247   257   

The median of these numbers is 131.

The third quartile (or upper quartile or 75th percentile) is the median of the upper half of the numbers. So, to find the third quartile, we need to place the numbers in value order and find the upper half.

37   60   64   65   73   87   87   87   93   128   134   138   145   158   164   194   205   219   247   257   273   284   341   353   362   371   385   387   461   467   489   498   522   531   551   640   888   966   1098   1108   

So, the upper half is

273   284   341   353   362   371   385   387   461   467   489   498   522   531   551   640   888   966   1098   1108   

The median of these numbers is 478.

The interquartile range is the difference between the third and first quartiles.

The third quartile is 478.

The first quartile is 131.

The interquartile range = 478 - 131 = 347.

Limit for the outliers are and