|
Q. 4. A computer while calculating the correlation
coefficient between 20 pairs of two variables x and
y obtain the following results: (Dec.
2001)
n = 20, å x = 100,
å y = 80, å
x2 = 520, å
y2 = 360, å
xy = 420
It was later discovered at the time of checking that
he had copied down two pairs as:
| x |
y |
While
the correct values were: |
x |
y |
|
6 |
4 |
8 |
12 |
|
8 |
6 |
6 |
8 |
Obtain the correct value of correlation coefficient.
Solution.
Here, n = 20, å
x = 100, å y = 80,
å x2 =
520, å y2
= 360, å xy = 420
| Incorrect pair |
|
Correct pair |
| x |
y |
x |
y |
| 6 |
4 |
8 |
12
|
| 8 |
6 |
6 |
8 |
Correct å x = 100
+ (8 - 6) + (6 - 8) = 100 (no change)
Correct å y = 80
+ (12 - 4) + (8 - 6) = 90
Correct å x2
= 520 + (82 - 62) + (62
- 82) = 520 (no change)
Correct å y2
= 360 + (122 - 42) + (82
- 62) = 516
Correct å xy =
420 + [(8 X 12) - (6 X 4)] + [(6 X 8) - (8 X 6)] =
492
| |
|
[(20 X 492) - (100 X 90)]
|
| r = |
|
|
| |
|
{[(20 X 520) - (100)2]
X [(20 X 516) - (90)2]}
|
or r = 0.893
|
