Statistics By Ihsan Ullah

Name Ihsan Ullah

Page No 1

Roll No 278

Question No 3.28 Find the average speed of the person who rides the first mile at the rate of 8 miles per hour, the next mile at the rate of 7.5 miles per hour and the third mile at the rate of 5.5 mile per hour. Data Given: 1st mile rate = 8miles/hour 2nd mile rate= 7.5miles/hour 3rd mile rate = 5.5 miles/hour Find Average Speed =?

X

1/ x

8

1/ 8

7.5

1/ 7.5 =

0.1333

5.5

1/ 5.5 =

0.1818

Calculated =

As we know:

Harmonic Mean=

∑x

∑ 1x

By putting the values in The Formula.

Harmonic Mean=

3

Harmonic Mean=

6.816 miles per hour

0.4401

0.125

Name Ihsan Ullah

Page No 2

Roll No 278

Question No 3.29 Find out the average of: Part 1. Motion in the case of a person who rides at the rate of 10 miles per hour, next mile at a rate of 3 miles per hour and the third mile at the rate of 6 miles per hour. In the above question we can easily see that the time is constant and speed is variable due to which the distance is also variable. So in this question the best way to calculate the mean is to use the harmonic Mean.

X (m/h) 10 8 6

1/x 1/10 1/8 1/6

As we know:

Harmonic Mean =

∑x

Harmonic mean= 3

∑ 1x

0.391

Harmonic mean= 7.672

Calculated 0.1 0.125 0.166

Name Ihsan Ullah

Page No 3

Roll No 278

Part 2. increase in the population in the first decade has increased 20% in the next decade 25% and in the third decade 44%. In this question the increase rate is in percentage so the best way to calculate the mean is to use Geometric mean. Lets suppose that at the beginning of the each year the population is 100 so at the end of the year the population will be Population in beginning+ percentage increase So X 120 125 144

Geometric mean = Antilog

Geometric mean = Antilog Geometric mean = Antilog Geometric mean = 125.89

LogX 2.07 2.09 2.15

∑ log x 6.31 3

2.10

n

Name Ihsan Ullah

Page No 4

Roll No 278

Question No 4.42 Compute the first movements about mean? Group Frequenc y Groups 2-4 4-6 6-8 8-10 10-12 12-14 14-16 16-18 18-20

2-4 18

ƒ 18 24 47 80 10 2 66 40 21 15 41 3

4-6 24

6-8 47

X 3 5 7 9 11

ƒ(x) 54 120 329 720 1122

(x- xbar) -7.76 -5.76 -3.76 -1.76 0.24

ƒ(x-xbar) -139.68 -138.24 -176.72 -140.8 24.48

ƒ(x-xbar)2 1083.91 796.26 664.46 247.80 5.87

ƒ(x-xbar)3 -8411.14 -4586.45 -2498.36 -436.12 1.40

ƒ(x-xbar)4 65270.44 26417.95 9393.83 767.57 0.336

13 15 17 19

858 600 375 285 4463

2.24 4.24 6.24 8.24 0

147.84 169.6 131.04 123.06 0

331.16 719.60 817.68 1018.46 5685.2

741.79 3048.98 5102.32 8392.11 1354.53

1661.60 12927.67 31838.47 69150.98 217428.846

∑∫ x

Mean=XBar=

XBar =

4463

413

XBar = 10.76

∑∫

8-10 80

10-12 102

12-14 66

14-16 40

16-18 21

18-20 15

Name Ihsan Ullah

M1 = M1 =

∑∫ x − xBar 0

Page No 5

∑∫

413

M1 = 0 M2 =

∑∫ ( x − xBar )

M2 = 5684.7

M2

∑∫

413

= 13.76

M3 =

∑∫ ( x − xBar )

M3

= 1354.53 413

M3

= 3.28

M4 =

∑∫ ( x − xBar )

M4 = 217428

413

M4

2

= 526.48

3

∑∫

4

∑∫

Roll No 278