Solution
Let for convenience of representation, x denote ERA and y represent Win%
[NOTE: Formulas and Answers are given below. Detailed Working follow at the end.]
Q1 Part (a)
First quartile, Q1 = average of the second and the third observation in the ordered set
= (0.022 + 0.026)/2
= 0.024
Third quartile, Q3 = average of the sixth and the seventh observation in the ordered set
= (0.028 + 0.030)/2
= 0.029
IQR = Q3 – Q1
= 0.005 Answer
Q1 Part (b)
Covariance = (1/n)Σ(i = 1, n){(xi – Mean X)(yi – Mean Y)}
= - 0.00027 Answer
Q1 Part (c)
V(X) = (1/n)Σ(i = 1, n)(xi – Mean X)2
V(Y) = (1/n)Σ(i = 1, n)(yi – Mean Y)2
Correlation coefficient = Covariance/sqrt{V(X).V(Y)}
= - 0.00027/(0.0049 x 0.0843)
= - 0.6653 Answer
Details of Working
Let for convenience of representation, dxi = (xi – Mean X) and dyi = (yi – Mean Y)
i |
x (ERA) |
y(Win%) |
dxi^2 |
dyi^2 |
(dxi)(dyi) |
1 |
0.028 |
0.53 |
1.40625E-07 |
0.00099225 |
-1.2E-05 |
2 |
0.021 |
0.542 |
4.38906E-05 |
0.00038025 |
0.000129 |
3 |
0.038 |
0.432 |
0.000107641 |
0.01677025 |
-0.00134 |
4 |
0.03 |
0.57 |
5.64063E-06 |
7.225E-05 |
2.02E-05 |
5 |
0.028 |
0.62 |
1.40625E-07 |
0.00342225 |
2.19E-05 |
6 |
0.022 |
0.74 |
3.16406E-05 |
0.03186225 |
-0.001 |
7 |
0.026 |
0.554 |
2.64062E-06 |
5.625E-05 |
1.22E-05 |
8 |
0.028 |
0.504 |
1.40625E-07 |
0.00330625 |
-2.2E-05 |
Total |
0.221 |
4.492 |
0.000191875 |
0.056862 |
-0.0022 |
Mean |
0.0276 |
0.5615 |
2.39844E-05 |
0.00710775 |
-0.00027 |
Square Root of Variance |
0.0049 |
0.0843 |
Ordered Set
0.021 |
0.022 |
0.026 |
0.028 |
0.028 |
0.028 |
0.03 |
0.038 |
DONE
19 ERA 20 Win% 21 0.021 0.028 0.028 0.530 0.038 0.432 0.03 0.022 0.026 0.554 0.028...
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