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Question 23 of 42
Q.

From the following information of heights of husband and wife, Calculate the rank correlation coefficient between their heights.

Height of husband (cms)156153185157163191162
Weight of wife (cms)154148162157162170154
Gujarat GsebGujarat Board (GSEB) HSC Commerce Board 2022Subjective· 5mImportance★★★★★
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Ranks give Σd2=4\Sigma d^2=4; wife's heights have two ties (each contributes 23−212=0.5\tfrac{2^3-2}{12}=0.5, total 11); r=1−6(Σd2+CF)n(n2−1)=1−30336≈0.911r=1-\dfrac{6(\Sigma d^2+\text{CF})}{n(n^2-1)}=1-\dfrac{30}{336}\approx\mathbf{0.911}.

Data (n=7n=7): Husband: 156,153,185,157,163,191,162; Wife: 154,148,162,157,162,170,154.

Assign ranks (rank 1 = tallest). Wife's value 162 occurs twice (ranks 2,3 → avg 2.52.5) and 154 occurs twice (ranks 5,6 → avg 5.55.5).

HusbandR1R_1WifeR2R_2d=R1−R2d=R_1-R_2d2d^2
15661545.50.50.25
1537148700
18521622.5-0.50.25
1575157411
16331622.50.50.25
1911170100
16241545.5-1.52.25
Σ4.00

Tie correction. For each group of mm tied ranks add m3−m12\dfrac{m^3-m}{12}. Wife has two groups of size m=2m=2: …

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