Question

. Seattle has a reputation of being a very rainy city. The total amount of rain for fourteen Septembers is listed below:

Year	Average
2003	0.81
2004	1.95
2005	0.99
2006	1.33
2007	2.20
2008	0.67
2009	2.30
2010	3.91
2011	1.12
2012	0.16
2013	5.26
2014	2.73
2015	1.46
2016	1.12

a. Is this data categorical or quantitative? If quantitative, is it discrete or continuous?

            b. Calculate the number of classes and class width.

            c. Construct a frequency distribution, including the classes, frequency, and relative frequency.

            d. Construct a histogram or bar graph (depending on your answer to part a), including all labels.

            e. Calculate the mean, median, and mode.

            f. Are the mean, median, and mode descriptive or inferential statistics?

            g. Calculate the range.

h. Calculate Q1.

i. Calculate Q3.

j. Calculate the IQR.

k. Find the variance.

            l. Find the standard deviation.

            m. Find the coefficient of variation.

            n. What is the 80^th percentile of this data set?

            o. Does this data set have any outliers? Use statistics in answering this question (not just your opinion).

            p. Would you use the Empirical rule or Chebyshev’s Theorem here and why?

            q. Based on the mean and median calculated above, would you expect this data to be symmetric, skewed to the left or skewed to the right and why?

Answer 1

a)Quantitavive and Continious

b)no of classes is 14

class width=1'

c)

year	frequency	relative frequency
2003	.81	3.11
2004	1.95	7.49
2005	.99	3.80
2006	1.33	5.11
2007	2.20	8.45
2008	.67	2.57
2009	2.30	8.84
2010	3.91	15.03
2011	1.12	4.3
2012	.16	.61
2013	5.26	20.22
2014	2.73	10.49
2015	1.46	5.61
2016	1.12	4.30

d)https://drive.google.com/drive/u/0/my-drive

e)

> mean(x)

[1] 1.857857

> median(x)

[1] 1.395

f) Discriptive statistics

g)  

range(x)

[ 0.16 , 5.26]

k ) Variance(x)=1.887557

h,j,n)

quantile(x,c(.25,.5,.75,.8))

25% 50% 75% 80%

1.0225 1.3950 2.2750 2.4720

I.e

h)Q1=1.0225

i) Q3=2.275

j)

IQR(x)

1.2525

l) standarad deviation =1.373884

m) cv=0.7394991

n)=80 percntile=2.4720

o)yes it has an out point measured by taking blox plot

p)chebshevs theorem

is used to find the proportion of observations you would expect to find within two standard deviations from the mean.

q) skewness value is 1.01

hence it is positevely skewed since

3*(mean(x)- median(x))/sd(x)=1.01