Question

Nora's math test results are listed. Find the meanand median. Round to the nearest tenth if necessary.Did the mean or median give a better overall scorefor Nora's performance?52%, 85%, 89%, 90%, 83%, 89%

Answer 1

We have the following scores:

52%, 85%, 89%, 90%, 83%, 89%

To calculate the median, we sort the scores from least to greatest:

52%, 83%, 85%, 89%, 89%, 90%.

As we have 6 scores, the median will be the average between the score that is in the third place and the score in the fourth place:

`\text{Median}=(x_3+x_4)/(2)=(85+89)/(2)=(174)/(2)=87`

The median is then 87%.

We can now calculate the mean as:

`\begin{gathered} M_{}=(1)/(n)\sum ^n_(i=1)\, x_i \\ M=(1)/(6)(52+85+89+90+83+89) \\ M_{}=(488)/(6) \\ M_{}\approx81.3 \end{gathered}`

The mean is 81.3%.

As 52% is an outlier that has a bigger effect in the mean than in the median, the median gives a better (higher) overall score for Nora's performance.

Also, the median is more representative of the set of data, as 52% can be considered an outlier.

Answer:

Median = 87%

Mean = 81.3%

The median gives a better overall score.