Respuesta :
The central measure Robert should use is given by: Option D: He should use the mean because there are no outliers that affect the mean.
How are mean and median affected if a value is changed to some other value?
The median is the middle value of the sorted(ordered in ascending or descending way)data values. If value changed is not the middle value (if number of observations are odd) or is not changing the average of two mid values (if number of observations are even), then the median won't change as it does't care about the value of the data unless its about the mid value of the sorted data or average of mid values.
How to determine unusual points (also called anomalies or outliers) ?
Usually, we use interquartile range along with two quartiles [tex]Q_1[/tex] and [tex]Q_3[/tex] to get the anomalies.
Those values which lie below [tex]Q_1 - 1.5\times \rm IQR[/tex] or above [tex]Q_3 + 1.5\times \rm IQR[/tex] are called anomalies, where IQR is inter Quartile Range, the difference between third and first quartile.
For the considered case, finding the quartiles and boundaries for anomalies:
Arranging the data in ascending order(might arrange in descending order too).
$250,000, $250,000, $267,000, $275,000, $300,000
- Median= Value which has equal number of observations on its either side = 267,000
- First quartile = Value left of which lies 25% of observations, and right of which lie about 75% of values = $250,000
- Third quartile = Value left of which lies 75% of observations, and right of which lie about 25% of values = $275,000
Thus, Inter Quartile Range(IQR) = difference between third and first quartile = 275,000-250,000= 25,000
Therefore, boundaries for anomalies= [tex][250000-1.5 \times 25000, 275000+1.5 \times 25000] = [212500, 312500][/tex]
All observations are under this range, so no outliers.
Since there are no outliers, mean can be used here.
Thus, He should use the mean because there are no outliers that affect the mean.
Learn more about outliers here:
brainly.com/question/10219729
