Question

A roller coaster operator kept track of the number of people who rode the roller coaster over a two week period. The data she collected is listed below:82, 72, 83, 76, 80, 76, 82, 73, 59, 79, 80, 78, 83, 81Part A: Determine if there is an outlier in this data set.Part B: If there is an outlier, describe how the mean is affected by the outlier in this data set.Part C: Explain why the Mean or the Median is the better representation of the data.

Answer 1

Given

Data as,

`82,72,83,76,80,76,82,73,59,79,80,78,83,81`

Find

(a) determine if there is an outlier in this data set.

(b) if yes, explain how the mean is affected

(c) Explain why mean or median is bettter representation of data.

Step-by-step explanation

As,we know if we subtract 1.5 * IQR from the first quartile, any values which are less than this number is consider as outlier,

similarly, if we add 1.5 * IQR to the third quartile, any values which are greater than this number is consider as outlier,

here, first quartile is 76, third quartile is 82 , IQR is 6

Lower fence = 76 -(1.5 *6 ) = 67

Upper fence = 82 -(1.5 * 6) =91

hence, the outlier is 59

B) the outlier decrease the mean

C) Both are better representation of the data

better to use mean when the distribution of the set is symmetrical an no clear outliers.

better toi use median when the distribution of the data is skewed and there are clear outlier