Assignment # 2
MTH302 (Spring 2012)
Total marks: 20
Lecture # 23 to 29
Due date:14-06-2012
Question No. 1:
In a Rice Mill the weights (in Kilograms) of 50 packets are given below:
| Observations | Frequency |
| 10 | 4 |
| 15 | 5 |
| 20 | 9 |
| 40 | 16 |
| 60 | 8 |
| 80 | 5 |
| 100 | 3 |
Find the Mean and Mode. Also, find the Median using the Empirical Relationships of Mean, Median and Mode.
Question No. 2:
Suppose that the manager of a company wants to know if there exists any correlation between the sales of the product A and the product B. Suppose that he selects a random sample of the total sales of these products in different days of the month. If you are a manager, then how will you calculate the correlation coefficient? (Use Manual Formula)
|
Days of the month |
Total sale of the product A |
Total sale of the product B |
|
1st day |
||
|
4th day |
||
|
7th day |
||
|
10th day |
||
|
15th day |
||
|
18th day |
||
|
22nd day |
||
|
25th day |
||
|
27th day |
||
|
30th day |
.
.
.
.
.
.
.
.
.
.
Idea Solution Hint:
mean=43.2
mode=40
median=40
correlation coefficient = 2.34
found these answers i am sharing. can any one plz share the formulas and solution according to these answers?
the following are the answers:
Mean=42.3
Median=16
Mode=the middle value of data= 5
ab in ka
Empirical Relationships of Mean, Median and Mode.
Mean= 21.5
Mode=1033.59
Median=86.9
Correlation coefficient = 0.77
……..
|
Observations (X) |
Frequency (F) |
FX |
|
10 |
4 |
40 |
|
15 |
5 |
75 |
|
20 |
9 |
180 |
|
40 |
16 |
640 |
|
60 |
8 |
480 |
|
80 |
5 |
400 |
|
100 |
3 |
300 |
|
ΣF = 50 |
ΣFX = 2115 |
Mean = ΣFX/ ΣF
= 42.3
Mode = 40
Median using Empirical Relation
Mean – Mode = 3(Mean – Median)
Median = 1/3[mode + 2mean]
= 1/3[40 + 2(42.3)]
= 41.533
|
Days of the month |
Total sale of the product A (X) |
Total sale of the product B (Y) |
XY |
X2 |
Y2 |
|
1st day |
15 |
16 |
240 |
225 |
256 |
|
4th day |
14 |
13 |
182 |
196 |
169 |
|
7th day |
10 |
11 |
110 |
100 |
121 |
|
10th day |
18 |
19 |
342 |
324 |
361 |
|
15th day |
15 |
13 |
195 |
225 |
169 |
|
18th day |
20 |
22 |
440 |
400 |
484 |
|
22nd day |
16 |
15 |
240 |
256 |
225 |
|
25th day |
15 |
17 |
255 |
225 |
289 |
|
27th day |
12 |
16 |
192 |
144 |
256 |
|
30th day |
13 |
17 |
221 |
169 |
289 |
|
|
148 |
159 |
2417 |
2264 |
2619 |