Question

Each of the following describes an *average* that someone might want to report or know. In each case, state whether they should prefer the mean or the median and one sentence on why. There may be multiple answers-your reasoning is important.
      
(i) A track coach wants to determine an appropriate heart rate for an *average* athlete during their workouts. She chooses five of her runners and asks them to wear heart monitors. In the middle of the workout, she reads the following heart rates for the five athletes: 130, 135, 140, 145, 325.
     
   *Write mean or median first and then give your reasoning starting on a separate line*
  
(ii) A journalist is writing an article, the main point of which is that an *average* professional basketball player is ridiculously over-paid.

   *Write mean or median and then give your reasoning starting on a separate line*

(iii) Middletown (pop 100,000 households) wants to know how much an *average* home in their town is worth, so they can estimate the total value of all the town's homes.

   *Write mean or median and then give your reasoning starting on a separate line*
  
(iv) A researcher wants to know the number of years an *average* patient with dementia lives after diagnosis.

*Write mean or median and then give your reasoning starting on a separate line*

Answer 1

(i)

Median

Reason: The data contains outlier: 325. For such skewed distribution,only median is to be used because median is not affected by outliers, whereas mean is susceptible by outliers,

(ii)

Median

Reason: The distribution of the pay of professional basketball player is highly skewed: Very few players have very high pay whereas the rest of them as low paid. For such skewed distribution,only median is to be used because median is not affected by outliers, whereas mean is susceptible by outliers,

(iii)

Median

Reason: The distribution of the value of the town's homes is highly skewed: Very few houses have very high value whereas the rest of them just normal value. For such skewed distribution,only median is to be used because median is not affected by outliers, whereas mean is susceptible by outliers,

(iv)

Median

Reason: The distribution of the value of the the number of years a patient with dementia lives after diagnosis is highly skewed: Very few patients live longer whereas the rest of them just normal value, since dementia is incurable. For such skewed distribution,only median is to be used because median is not affected by outliers, whereas mean is susceptible by outliers,