Answer: Choice B
The mean is less than the median
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Explanation:
Let's say that this class has 20 students. Half of which got a score of 78, so that means 20/2 = 10 students got this score.
There are 20-10 = 10 students left.
Now let's say that 2 people got a score of 55. That means 10-2 = 8 students got 74.
We have
The total sum of all those scores is 10*78+2*55+8*74 = 1482 in which divides over the number of scores overall (20) to get 1482/20 = 74.1
The mean of this data set is 74.1
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Now let's find the median
This is our data set
{55,55,74,74,74,74,74,74,74,74,78,78,78,78,78,78,78,78,78,78} which is honestly a mess and it's easy to get lost here.
Basically I listed two copies of 55, eight copies of 74, and ten copies of 78
You should find that because there are n = 20 items here, the median is between slot n/2 = 20/2 = 10 and slot 11. Those two values in those slots are 74,78 in that exact order.
Average those two values to get (74+78)/2 = 76
The median is 76
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The mode is the quickest to find. It's simply the most frequent value, which is 78. It occurs the most of any other value.
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To recap, we have these three items
We'll use these items to go through the four answer choices given.
We see that choice A is false because the mean is not greater than the mode.
Choice B is true and it's the final answer because the mean is less than the median. This is due to the fact that the 55's are somewhat outliers that pull down the mean score to be less than the median.
Since choice B is true, this rules out choice C and choice D as well.
