Three friends Aravind- Rahul and Nikhil rated 5 movies as tabulated below- Which two of them has the most similar tastes in movies-WhineMovies - Aravind - Rahul - Nikhil WhlineM1- 5-5 - 6-5 - 7 1Nhline M2 - 6-5 - 8-5 - 8 Illhline M3 - 8-5 - 5 - 6-5 INhlineM4- 4 - 7 -7-5 11 hlineM5 - 7 - 6 - 10 wllhlineendarray A- Rahul and NikhilB- Aravind and NikhilC- Cannot be concludedD- Aravind and Rahul

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Spearman's Rank Coefficient for Quantitative Data

Three friends...

Question

Three friends Aravind, Rahul and Nikhil rated 5 movies as tabulated below. Which two of them has the most similar tastes in movies?

$\begin{matrix} M o v i e s & A r a v i n d & R a h u l & N i k h i l M_{1} & 5.5 & 6.5 & 7 M_{2} & 6.5 & 8.5 & 8 M_{3} & 8.5 & 5 & 6.5 M_{4} & 4 & 7 & 7.5 M_{5} & 7 & 6 & 10 \end{matrix}$

Aravind and Rahul

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Rahul and Nikhil

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Aravind and Nikhil

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Cannot be concluded

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Solution

The correct option is B
Rahul and Nikhil

Convert the ratings of Aravind and Rahul to corresponding ranks and calculate deviations.

$\begin{matrix} M o v i e s & A & R & D_{i} = A - R & D_{i}^{2} M_{1} & 4 & 3 & 1 & 1 M_{2} & 3 & 1 & 2 & 4 M_{3} & 1 & 5 & - 4 & 16 M_{4} & 5 & 2 & 3 & 9 M_{5} & 2 & 4 & - 2 & 4 \sum = 34 \end{matrix}$

$r_{k} = 1 - \frac{6 \sum D_{i}^{2}}{n^{3} - n} = 1 - \frac{6 \times 34}{125 - 5} = 1 - \frac{204}{120} = - 0.7$

Convert the ratings of Rahul and Nikhil to corresponding ranks and calculate deviations.

$\begin{matrix} M o v i e s & R & N & D_{i} = R - N & D_{i}^{2} M_{1} & 3 & 4 & 1 & 1 M_{2} & 1 & 2 & - 1 & 1 M_{3} & 5 & 5 & 0 & 0 M_{4} & 2 & 3 & - 1 & 1 M_{5} & 4 & 1 & 3 & 9 \sum = 12 \end{matrix}$

$r_{k} = 1 - \frac{6 \sum D_{i}^{2}}{n^{3} - n} = 1 - \frac{6 \times 28}{125 - 5} = 1 - \frac{72}{120} = 0.4$

Convert the ratings of Aravind and Nikhil to corresponding ranks and calculate deviations.

$\begin{matrix} M o v i e s & A & N & D_{i} = A - N & D_{i}^{2} M_{1} & 4 & 4 & 0 & 0 M_{2} & 3 & 2 & 1 & 1 M_{3} & 1 & 5 & - 4 & 16 M_{4} & 5 & 3 & 2 & 4 M_{5} & 2 & 1 & 1 & 1 \sum = 22 \end{matrix}$

$r_{k} = 1 - \frac{6 \sum D_{i}^{2}}{n^{3} - n} = 1 - \frac{6 \times 22}{125 - 5} = 1 - \frac{132}{120} = - 0.1$

Clearly, Rahul and Nikhil have the most similar taste in movies.

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Similar questions

The ratings of 6 laptops in two websites A and B are given below. Find the rank coefficient for the ratings of the two websites.

$\begin{matrix} L a p t o p s & A & B L_{1} & 7 & 8 L_{2} & 8.5 & 9.5 L_{3} & 9.5 & 8 L_{4} & 8 & 8 L_{5} & 8.5 & 6.5 L_{6} & 7.5 & 7.5 \end{matrix}$

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Three friends Aravind, Rahul and Nikhil rated 5 movies as tabulated below. Which two of them has the most similar tastes in movies? MoviesAravindRahulNikhilM15.56.57M26.58.58M38.556.5M4477.5M57610