During contract negotiations, a company seeks to change the number of

Carole Yarbrough

Carole Yarbrough

Answered question

2021-12-08

During contract negotiations, a company seeks to change the number of sick days employees may take, saying that the annual “average” is 7 days of absence per employee. The union negotiators counter that the “average” employee misses only 3 days of work each year. Explain how both sides might be correct, identifying the measure of center you think each side is using and why the difference might exist.

Answer & Explanation

Jordan Mitchell

Jordan Mitchell

Beginner2021-12-09Added 31 answers

Step 1 
Definition. The sample mean x of observations x1, x2,xn is given by 
x=x1+x2++xnn=1ni=1nxi 
Definition. The sample median x isproduced using n observations that are sorted from the smallest to the biggest, including repeated values, as
x¯={The only middle value if n is oddThe average of the two middle values if n is even  
x¯={(n+12)th,if n is oddaverage of(n2)thand(n2+1)thordered values,if n is even  
The sample median of sick days is used by one party, most likely the firm, while the sample mean is used by the other. Given that the distribution is most likely right biased, the mean should be higher. Couple employees use several sick days, and the majority of them only take a few.
The union utilized the sample median; the company used the sample mean as the response.

Suhadolahbb

Suhadolahbb

Beginner2021-12-10Added 32 answers

Step 1 Since most individuals only get sick for a few days a year, the distribution will be right-skewed due to the small number of persons who are unwell for an extended period (more than a week).
We may predict that the median will be lower than the mean for a right-skewed distribution because the mean is heavily impacted by the few individuals who have prolonged illness, but the median is not.
As a result, the mean is the yearly average of 7 days, while the median is the annual average of 3 days.
Solution: "Mean" 7 days
3 days in Mwdian.

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