Statistics and Probability (STA301)- Solution of Practice Questions Lecture No 6 to 10

Numerical Questions

(Sample questions)

Q1: Use the decimal part in each value as the leaf and rest of the digit as stem to construct the stem-and-leaf table for the following 15 values.

 6.1, 7.9, 8.0, 5.9, 5.2, 1.2, 3.5, 4.6, 1.9, 2.6,   4.4, 7.3, 4.2, 5.1, 4.9

Answer:

Stem	Leaf
1	2,9
2	6
3	5
4	2,4,6,9
5	1,2,9
6	1
7	3,9,8

Q2: If Mean = 35.4, and Mode = 32.1, find the value of median?

Answer:

Mode = 3 Median – 2 Mean

32.1 = 3 * Median – 2 * 35.4

32.1 = 3Median – 70.8

3Median = 70.8+32.1

3Median = 102.9

Median = 102.9/3

Median = 34.3

Q3; Calculate Arithmetic Mean for the following data:

Classes	10-14	15-19	20-24	25-29	30-34	35-39
Frequency	2	4	6	8	3	1

Answer:

Class	Frequency	Mid Point
	f	X	fx
10-14	2	12	24
15-19	4	17	68
20-24	6	22	132
25-29	8	27	216
30-34	3	32	96
35-39	1	37	37
Total:	24		573

Arithmetic Mean        =total of fx/Total f

                                    = 573/24

                                    =23.88

Q4: A person computed the values of A.M, G.M, and H.M and recorded unsystematically as 23.47, 24.00 and 22.90. Identify the values of A.M, G.M, and H.M.

Answer:

We know that relation between the A.M, G.M. and H.M. is as follow:

Arithmetic Mean > Geometric Mean >Harmonic Mean

So,

A.M.=24.00

G.M.=23.47

and                  H.M.= 22.90

Q5: If the mean of the following frequency distribution is 3.66, find the value of median.

X	1	2	3	4	5	6
f	3	9	12	11	8	7

Answer:

From the table, the total frequency is 50

As 50 is the even number then the mode is x at 25 and 26 which is on both positions.

Therefore

Median = (4+4)/2 = 8/2 = 4

Q6: A Vehicle going up from Lahore to Murree consumes petrol at the rate of One liter per 8 kms, while going from Muree to Lahore one Liter per 12 kms. Find the average rate consumption between the two cities.

Answer:

X	1/X
8	0.125
12	0.083333
Total	0.208333

H.M = n/∑(1/X)

n=2

∑(1/X) = 0.208333

H.M = 2/0.20833

H.M = 9.6 km/litre

Q7:  Using the basic definition, compute G.M from the following values:

0.5, 1.0, 2.7, 3.48, 4.71. Also verify the results using the logarithmic method.

Answer:

G.M.    = (0.5*1.0*2.7*3.48*4.71)^(1/5)

            = (22.12758)^(1/5)

            =1.857748

Verify by using Logarithmic Method:

X	log X
0.5	-0.30103
1	0
2.7	0.431364
3.48	0.541579
4.71	0.673021
Total:	1.344934

           

log G.M.          =          log ∑x/n

                        =          1.344934/5

                        =          0.268987

G.M.                =          anti log 0.268987

                        =          (10)^0.268987

GM                        =          1.857748