Answer:
The safer option, would be to pick Yolanda, because of the lower risk involved. It is certain that she would score in and around the mean.
But, if one is a betting man, the rewards from Tobin performing to the favourable side of his wider range of possible scores would guarantee a higher mark. Although, there's an equal likelihood that Tobin's scores might tilt towards the unfavourable side.
Step-by-step explanation:
The mean absolute deviation (MAD) and the inter quartile range (IQR) both serve to highlight the spread variables in the dataset about the mean.
The higher their respective values, the more the variation of the variables in the dataset. It means
A high MAD and IQR indicate that the possible different obtainable scores from the candidate can take on values from extreme lows to extreme highs all around the mean, a wider range of possible scores.
This translates to the fact that Tobin's scores, which have a clearly superior MAD and IQR, have a higher risk attached to them. It is possible the scores in the exam take on values much lower than the mean or values much higher than the mean.
Yolanda on the other hand, has a lower MAD and IQR, thereby indicating a narrower range of possible values for her scores. This means that her scores will hover in and around the mean without big variations.
Yolanda's scores have a lower risk attached to them as it is guaranteed thay she would score close to their common mean score.
But Tobin's scores have a high risk and high reward attached to them. Going with Tobin would mean that one is ready to expect a score from a wider range about the mean.
Tobin could spectacularly post scores that are very much more than their mean score or post scores that are way worse than their mean score.
So, the choice of who to pick depends on which approach one takes to this subject matter.
Minimum Highest loss would mean Yolanda is safer and a better option.
Maximim Highest gain would mean Tobin is worth the risk and might be a better option.
Hope this Helps!!!
