Question

4. The life expectancy of a person in 24 randomly selected countries for the year 2011 is in the table below.

   a.) What is the range of the life expectancy rates? b.) What is the median of the life expectancy rates?

   77.2	55.4	69.9	76.4	75.0	78.2
   73.0	70.8	82.6	68.9	81.0	54.2

   5) Cholesterol levels were collected from patients two days after they had a heart attack and are shown in the table below. (Show all work. Just the answer, without supporting work, will receive no credit.)

   270	236	210	142	280	272	160
   220	226	242	186	266	206	318
   294	282	234	224	276	282	360
   310	280	278	288	288	244	236

   1. a.) What is the sample mean?

   2. b.) What is the sample standard deviation? (Round your answer to two decimal

      places.

   3. 6) There are 4 black marbles and 6 red marbles in a box. Consider selecting one marble at a time from the box. What is the probability that the first marble is black and the second marble is also black. Express the probability in fraction format. (Show all work. Just the answer, without supporting work, will receive no credit.) a.) Assume the marble is selected with replacement. b.) Assume the marble is selected without replacement.

Answer 1

( 4 )

Range :

Ordering the data from least to greatest, we get:

54.2   55.4   68.9   69.9   70.8   73.0   75.0   76.4   77.2   78.2   81.0   82.6   

The lowest value is 54.2.

The highest value is 82.6.

The range = 82.6 - 54.2 = 28.4.

The range of data set is 28.4.

Median :

The median is the middle number in a sorted list of numbers. So, to find the median, we need to place the numbers in value order and find the middle number.

Ordering the data from least to greatest, we get:

54.2   55.4   68.9   69.9   70.8   73.0   75.0   76.4   77.2   78.2   81.0   82.6   

As you can see, we do not have just one middle number but we have a pair of middle numbers, so the median is the average of these two numbers:

Median = ( 73.0+75.0) / 2 = 74

The median of the data set is 74.

( 5 )

( a )  sample mean = Sum of terms / Number of terms

= 7110 / 14

= 253.9286

( b )  sample standard deviation :

Create the following table.

data	data-mean	(data - mean)2
270	16.0714	258.28989796
236	-17.9286	321.43469796
210	-43.9286	1929.72189796
142	-111.9286	12528.01149796
280	26.0714	679.71789796
272	18.0714	326.57549796
160	-93.9286	8822.58189796
220	-33.9286	1151.14989796
226	-27.9286	780.00669796
242	-11.9286	142.29149796
186	-67.9286	4614.29469796
266	12.0714	145.71869796
206	-47.9286	2297.15069796
318	64.0714	4105.14429796
294	40.0714	1605.71709796
282	28.0714	788.00349796
234	-19.9286	397.14909796
224	-29.9286	895.72109796
276	22.0714	487.14669796
282	28.0714	788.00349796
360	106.0714	11251.14189796
310	56.0714	3144.00189796
280	26.0714	679.71789796
278	24.0714	579.43229796
288	34.0714	1160.86029796
288	34.0714	1160.86029796
244	-9.9286	98.57709796
236	-17.9286	321.43469796

∑(xi−X bar )²=61459.8571

S = sqrt( 61459.8571 / 27 )

= 47.7105

S = 47.71