3. The mean is the sum of numbers divided by the number of numbers. It is the same as the average.
You have 2 columns of numbers. You are asked to find the mean of each of them. Add them up and divide by 6, the number of numbers in each column.
... (45 + 32 + 25 + 75 + 60 + 50)/6 = 47.83 . . . group 1 mean
... (39 + 72 + 65 + 90 + 55 + 120)/6 = 73.5 . . . .group 2 mean
Now, you are asked to decide which of these is the larger number and how it relates to the number of text messages sent. My observation is ...
... Group 2 had the higher mean time spent on homework, so apparently group 1 was more efficient at doing homework.
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4. Mean vs. median questions are always a bit tricky. They tend to be political as much as mathematical, especially when it comes to numbers that are socially important--such as housing prices.
If you examine this data, you find the lower quartile is 780,000 and the upper one is 840,000, so the inter-quartile range is 60,000. The value 455,000 lies several times this number below the lower quartile of 780,000, so can be considered to be an outlier. As such it will tend to make the mean somewhat lower than it would be if that outlier were ignored.
This suggests that the mean of this dataset may not fairly represent the bulk of the data in the dataset. That is, if you're a home buyer with sufficient cash to purchase a house of average price (762,000), you will find you can only purchase the house with the lowest price--because all the others are well above the average (780,000 and higher). The median price (800,000) may represent these home prices best.
On the other hand, if you're a tax planner, your tax revenue will depend on the total value of houses in the neighborhood. That is, the mean value will be the best choice for your calculation purposes. If you calculate based on the median value, you will significantly overestimate your tax revenue.
My point here is that the answer depends on the use the numbers will have. You need to decide an appropriate use, and choose mean vs. median accordingly—or explain why each has its uses, as I have done here.
