2. Consumer Reports provides performance and quality ratings for numerous consum

Question

2. Consumer Reports provides performance and quality ratings for numerous consumer products. The overall ratings (score) were provided for a sample of 7 mid-priced VCRs in the Consumer Reports 1992 Buying Guide. The manufacturer brands and overall scores are as follows: lanufacturer Fisher iencral Electrie2 itach 105 lontgomery Ward 2078 a. determine the sample mean, median, variance and standard deviation for the variable Price b. determine the 90th percentile, the first quartile and the IQR for the variable Price c. determine the coefficient of variation for the variable Price; d compute the z-score's for the variable Price;

Explanation / Answer

### By using R software:

> Price=c(75,82,105,86,89,73,70)
> Price
[1] 75 82 105 86 89 73 70
> Score=c(77,81,89,78,78,80,78)
> Score
[1] 77 81 89 78 78 80 78
> n=length(Price)
> n ## sample size
[1] 7
> Xbar=mean(Price)
> Xbar ### sample mean
[1] 82.85714
> V=var(Price)
> V### Sample variance
[1] 143.8095
> S=sd(Price)
> S #### Sample standard deviation
[1] 11.99206
> summary(Price)
Min. 1st Qu. Median Mean 3rd Qu. Max.
70.00 74.00 82.00 82.86 87.50 105.00
> m=median(Price)
> m
[1] 82
> Q=quantile(Price,c(0.90,0.25))
> Q ### Sample quartile
90% 25%
95.4 74.0
> I=IQR(Price)
> I ### Interquartile range
[1] 13.5
> C=(S/Xbar)*100
> C ## coefficient of variation
[1] 14.47318
> Z=(Price-Xbar)/(S/sqrt(n))
> Z ### Z score
[1] -1.7334840 -0.1891073 4.8852732 0.6933936 1.3552693 -2.1747345 -2.8366102
> cov(Price,Score)### sample covariance
[1] 38.19048
> cor(Price,Score)### correlation coefficient
[1] 0.7691652

Here Correlation coefficient is 0.77 which indicates that there is positive relationship between Price and score. That is increase in price results in increase in score and vice versa.

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