variable in context d ctriking deviations nALAN aguantitative from MEASURES OF C

Question

variable in context d ctriking deviations nALAN aguantitative from MEASURES OF CENTER (THE MEDIAN) Learning Objectives * e . Summarize and describe the distribution of a quantitative variable in context Relate measures of center and spread to the shape of the distribution Based on the shape of a distribution of data, determine whether to use the median or the mean as the measure of central tendency This example is used to ilustrate the difference between the two different the mean and the medion, Let's imagine that the salaries of the patrons currently eating at a local diner (before Bill Gates walks in) are given below Patron Anna Bob Cathy Dave Eric Fran Salary $30,000 $75,000 $55,000 $55,000 $30,000 $85,000 Gail $35,000 30405060708090 Annual Salary (S in thousands) 1) Find the mean and median salary before Bill Gates walks into the diner Are the two measurements close? Would they represent a typical customer's salary? Which would you choose to represent a typical customer's salary? 2)

Explanation / Answer

Mean= (30,000+75,000+55,000+55,000+30,000+85,000+35,000)/7

Mean= 365000/7= 52142.86

Median Step 1: Place the data in ascending order. In other words, sort your data from the smallest number to the highest number. For this sample data set, the order is:

Step 2: Find the number in the middle (where there are an equal number of data points above and below the number):
$55000

2) The two measurments are slightly close. Yes they represent a typical customer's salary. I would choose median because it does not disturb by outliers.

30000 30000 35000 55000 55000 75000 85000

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