Statistics ( Statistical methods HW)

Statistical Methods (STAT-4303)

Fall, 2015

Instructor: Dr. Rajan Lamichhane

HW-2

Total Points: 55

Q.1 Summation notation: [2x8=16]

(a) Let An = {1, 3, 5, 7, 9}. What is the value of a3 ?

(b) Find the value of :

(i)  

5

1i

n A

(ii)  

5

3i

n A

(iii)  

5

1i

n A +3

(iv) )3( 5

1

 i

n A

(v)  

5

1

2 i

n A

(vi) )3(2 5

1

 i

n A

(vii)  

5

1

2 i

n A +3

Q.2 If Xi=2i and P(X=i)= 4

i for i=0, 1, 2, 3 . Find the value of E(X) where

)()( 0

i

n

i

i xXPXXE 



 . [5]

Q.3. [2x6=12]

The data represent the number of days off per year for a sample of individuals selected from nine

different countries.

20,26,40,36,23,42,35,24,30

Find (a) mean

(b) median

(c) Q1

(d)Q3

(e) mode

(f) Plot box plot and comment about the shape of the distribution.

Q.4. [2x11=22]

The data below represents the test scores obtained by students in college algebra class.

2,3,4,3,3,3,4,5,5,5,5,5,6,6,6,6,6,6,7,7,8,8,9,9,9,10

(a) Create a frequency table

(b) Find the mean

(c) What is the median of the data

(d) Find first (Q1) and 3 rd (Q3) quartiles.

(e) Plot box plot(Box plot is also called Box and Whisker plot)

(f) From box plot what can you say about the shape of the distribution

(g) Find the mode

When recording the above grades in EXCEL, teaching assistant had mistakenly reported

10 as 100 then

(h) What will happen to the mean? Will it increase, decrease or remains the same?

(i) Find the new mean (replacing 10 by 100 in the above data)

(j) What will be the new median?

(k) What can you say about the effect of outliers on mean and median?

Q.5. Find the mean age of freshmen students from the following table: [5]

Age (x) Number

of

students

(f)

16 3

17 4

18 2

19 1

20 5

21 1

22 1

Q.6. The following table shows the number of miles run during one week for a sample of 20

runners: [5]

Miles Frequency

5.5-10.5 1

10.5-15.5 2

15.5-20.5 3

20.5-25.5 5

25.5-30.5 4

30.5-35.5 3

35.5-40.5 2

Calculate the average (mean) miles run.

Q.7. (a) If the mean of 15 observations is 20.5, find the sum of all observations? [2+5=7]

(b) Use the following data

1.5, 10.2, 14.1, 14.4. 14.4, 14.4, 14.5, 14.5, 14.6, 14.7, 14.7, 14.7, 14.9, 15.1, 15.9, 22.5,

36.4

and find Q1, Q3 and IQR. Then find the possible outliers if any?