Statistical Analysis

Statistical Analysis

Test 1

Question 01

Construct a frequency polygon from the following frequency distribution.

Temperature

Frequency

28.5-31.5

1

31.5-34.5

3

34.5-37.5

6

37.5-40.5

10

40.5-43.5

8

43.5-46.5

7

Solution

Frequency Polygon

In Statistics, it's a graph that made by joining all the top points of the histogram bars. By joining all the top points, we obtain a shape that defines the position of the values (Miller, et.al, 1965).

By using the above data, first we have to find out mid points and cumulative frequency of the observation that helps to find out the frequency polygon curve(Goulden, 1939).

Class Boundaries

Lower

Upper

Midpoints

Frequency

Cumulative Frequency

28.5

31.5

30

1

1

31.5

34.5

33

3

4

34.5

37.5

36

6

10

37.5

40.5

39

10

20

40.5

43.5

42

8

28

43.5

46.5

45

7

35

Mid Point

It is obtained by adding the lower limit and upper limit value, and the divide by 2. The formula of mid point is

Where UL = Upper Limit

LL = Lower Limit

Cumulative Frequency

It is a total of frequency and all frequencies. By adding all the frequency step by step we found the cumulative frequency value (Raiffa & Schlaifer, 1961).

Frequency Polygon Data

27

0

30

1

33

3

36

6

39

10

42

8

45

7

Frequency Polygon data has obtained by adding one midpoint and frequency value in the given data.

The Frequency Polygon curve has defined the negative skewed shape because it's start with origin and has long tail.

Question 02

The costs per load (in cents) of 27 dish-washing detergents tested by a consumer organization are shown here.

Class limits

Frequency

20-28

4

29-37

11

38-46

2

47-55

10

Find the mean.

Find the standard deviation.

Solution

Class limits

Frequency f

Mid Point Xm

f. Xm

Xm^2

f.Xm^2

20-28

4

24

96

576

2304

29-37

11

33

363

1089

11979

38-46

2

42

84

1764

3528

47-55

10

51

510

2601

26010

 

?f = 27

 

?f. Xm = 1053

 

?f.Xm^2 = 43821

Mean

Variance

Standard Deviation

Question 03

Consider the following data set: 12, 16, 18, 17, 15, 22, 14, 30, 13a)Find the mean.b)Find the standard deviation.

Solution

Data

12

16

18

17

15

22

14

30

13

X

X^2

12

144

16

256

18

324

17

289

15

225

22

484

14

196

30

900

13

169

SUM

157

2987

Mean

Variance

/8

Question 04

You are answering three multiple-choice questions. Each question has five answer choices, with one correct answer per question. If you select one of these five choices for each question and leave nothing blank, in how many ways can you answer the questions?

Solution

Each question has 5 possible outcomes for an answer

Question 1st = 5 possible ways

Question 2nd = 5 possible ways

Question 3rd = 5 possible ways

Total number of possible answers can be determining by multiplying all the three possible outcomes of three days.

Total number of ways = 5 * 5 * 5

Total number of ways = 125 ways

Hence 125 are the total number of ways that can use for answer the questions (Freund & Simon, 1967).

Question 05

A box contains five red balls, six green balls, and nine yellow balls. Suppose you select one ball at random from the box and do not replace it. Then you randomly select a second ball. Find the probability that both balls selected are red.

Solution

Number of ways red balls can occur = 5

Number of ways green balls can occur = 6

Number of ways yellow balls can occur = 9

Total number of balls occur = 20

From the red ball, one ball has lost and now total number of red balls is 4 and the possible outcomes are 19 (Berger, 1985).

Probability of red balls: P(r) = 4/19

The total probability of both selected red balls is = (4/19) (5/20)

= (20/20 *19)

= 1/19

Hence the probability of both selected red balls is 1/19

Question 06

One card is randomly selected from a standard deck of cards. Find the probability of selecting a black card or a ...