Question

The accompanying data represent the miles per gallon of a random sample of cars with a three-cylinder, 1.0 liter engine.

(a) Compute the z-score corresponding to the individual who obtained 36.3 miles per gallon. Interpret this result.

(b) Determine the quartiles.

(c) Compute and interpret the interquartile range, IQR.

(d) Determine the lower and upper fences. Are there any outiers?

Answer 1

A)

	X	(X - X̄)²
total sum	935.3	295.59
n	24	24

mean =    ΣX/n =    935.3/24=   38.97
sample std dev =   √ [ Σ(X - X̄)²/(n-1)] =   √(295.5896/23)=   3.58

X=   36.3  

Z=(X-µ)/σ= (36.3-38.97)/3.58=       -0.75

............

quartile , Q1 = 0.25(n+1)th value=   6.25th value of sorted data=   36.68

Q2 = 0.5(n+1)th value =    12.5th value of sorted data=   38.45
      
Quartile , Q3 = 0.75(n+1)th value=   18.75th value of sorted data=   41.30

..................

      
IQR = Q3-Q1 =    41.3-36.675=   4.63

      

A. The interquartile range is mpg. It is the range of the middle 50% of the observations in the data set.

/..............

1.5IQR = 6.94  
      
lower bound=Q1-1.5IQR=   29.74  
upper bound=Q3+1.5IQR=   48.24  

THERE IS 1 OUTLIER (49.3)

.................

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