Of the sample of 1000 gas prices assume the mean price of 99

Of the sample of 1,000 gas prices, assume the mean price of 999 gas stations is $3.95 and the range is $0.85. One gas station had a promotional giveaway of gas the day of the survey, and reported a price of $0 (the only such price in the sample). How would that single value affect the following:

i)    Skewness of the distribution

ii)   Kurtosis of the distribution

iii)   Standard deviation

Solution

The value of $0 would be an outlier for the data.

iii) Standard devaition of the data increases due to any outlier in the data.Thus, the standard deviation in the data would increase

ii)Skewness shows how the data is concentrated.

The value of the outlier pulls the distribution towards itself

Thus, the value of zero will pull the data towards itself and we will have a negative skewness in the distribution

i)

Kurtosis defines the peakedness in the data.

Any addition in the extreme values will make the tails fatter and the peak narrower and sharper.

Same is the case with the zero. Since, it is an extreme value, the Kurtosis would increase and we will have a sharper peak and so more positive kurtosis.

Hope this helps.