Question

Consider a sample with 10 observations of 11, –3, 8, 8, 10, 1, –2, 13, 8, and –4. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution. (Round your answers to 2 decimal places. Negative values should be indicated by a minus sign.)

The z-score for the smallest observation
The z-score for the largest observation
There are outliers or no outliers in the data.

The historical returns on a portfolio had an average return of 21 percent and a standard deviation of 29 percent. Assume that returns on this portfolio follow a bell-shaped distribution.

a.	Approximately what percentage of returns were greater than 79 percent? (Round your answer to the nearest whole percent.)

b.	Approximately what percentage of returns were below –66 percent? (Round your answer to 1 decimal place.)

The following relative frequency distribution was constructed from a population of 400. Calculate the population mean, the population variance, and the population standard deviation. (Negative values should be indicated by a minus sign. Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Class	Relative Frequency
−20 up to −10	0.14
−10 up to 0	0.22
0 up to 10	0.32
10 up to 20	0.32

Population mean
Population variance
Population standard deviation

Thirty-nine cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution.

Vacancy Rate (in percent)	Frequency
0 up to 3	7
3 up to 6	4
6 up to 9	9
9 up to 12	6
12 up to 15	13

a.	Calculate the average vacancy rate. (Round your answer to 2 decimal places.)

b.	Calculate the variance and the standard deviation for this sample. (Round your intermediate calculations to 4 decimal places and final answers to 2 decimal places.)

Variance
Standard deviation

The National Sporting Goods Association (NSGA) conducted a survey of the ages of people that purchased athletic footwear in 2009. The ages are summarized in the following relative frequency distribution. Assume the survey was based on 100 individuals.

Age of Purchaser	Percent
Under 14 years old	14
14 to 17 years old	9
18 to 24 years old	12
25 to 34 years old	14
35 to 44 years old	15
45 to 64 years old	22
65 years old and over	14

a.	Calculate the average age of this distribution. Use 10 as the midpoint of the first class and 75 as the midpoint of the last class. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

b.	Calculate the sample standard deviation. (Round your intermediate calculations to 4 decimal places and final answer to 2 decimal places.)

Answer 1

1. Solution:

Given data :

sample of observations n =10

observations = 11, –3, 8, 8, 10, 1, –2, 13, 8, and –4

Now, we have to find out the :

Use z-scores to determine if there are any outliers in the data:

To use z- score method 1st we have to find the mean standard deviation

Mean:

Formula for the mean is ,

Mean = Sum of observations / no .of observations

=(11 –3+8+8+10+ 1–2+13+ 8-4 ) /10

= 5

Mean = 5

Standard deviation = $\sqrt{} \frac{ \sum(_x{i} - x)^{2}}{n}$

$\sqrt{} \frac{( 11- 5)^{2}+ (-3-5)^{2}+( 8-5)^{2}+(8-5)^{2}+(10-5)^{2}(1-5)^{2}(-2-5)^{2}+(13-5)^{2}+(8-5)^{2}(-4-5)^{2}}{10}$

= $\sqrt{} \frac{36+ 64+9+9+25+16+49+64+9+81}{10}$

= $\sqrt{} \frac{362}{10}$

=$\sqrt{} 36.2$

= 6.016

Standard deviation = 6.016

We know $z = \frac{_x{i}-x}{s}$

now

x	11	-3	8	8	10	1	-2	13	8	-4
$z = \frac{_x{i}-x}{s}$	(11-5)/6.0 = 1	(3-5)/6.0 =-0.033	(8-6)/6.0 0.333	(8-6)/6.0 = 0.333	10-6)/6.0 = 0.666	(1-6)/6.0 = -0.833	(-2-6)/6. = -1.333	(13-6)/6.0 = 1.166	(8-6)/6.0 = 0.333	(-4-6)/6.0 = -1.666

Based on the s values we can consider as,

By watching the z - scores estimations of the given information It is clear that, there are

" no outliers " exists in the given information.

Note: As per the HOMEWORKLIB RULES, three questions are enough. so i am not answer the question 2 and 5 . if you want remaining questions please re upload as another question.

Thank you,