Question: TV Frequencies - Question III

Since there is an EVEN number of values (there are 150 values), the median will equal the average of the 75th and 76th values (for more on this, watch https://www.greenlighttestprep.com/module/gre-statistics/video/800). The 75th value is 2 and the 76th value is 3. So, the median = (2 + 3)/2 = 2.5

Can you explain your approach?

We have a couple of options.

One approach is to first recognize that, since we have an even number of values (150 values), the median will equal the average of the two middlemost values.

If we arrange the 150 values in ascending order, the values will look like this:

{smallest 74 values, 1st middle value, 2nd middle value, biggest 74 values}

From this, we can see that the two middlemost values will be the 75th and 76th values.

Alternatively, we can say that, if there are k values, and k is EVEN, then the two middlemost values (when arranged in ascending order) will be the k/2 value and the (k/2)+1 value.

So, for example, if there are 66 values in total, then the two middlemost values will be the 33rd value and the 34th value.

Q: Assuming there were 3 families that had 6 or more televisions, the median would have been based on the odd number in the middle of the listings, right?

A: If there were 3 families that had 6 or more televisions, then the total number of data values would be 153

In this case, the median would equal the 77th number (when all the numbers are arranged in ascending order)

So, the median would be 3

Q: The reason we excluded that group is because no family in Townville owns 6 or more televisions.

A: That's correct.

If we arrange a bunch of values in ascending order, then the median is the middle value. If there are two middle values (as is the case when there is an even number of values), then the median is the average of the two middle values.

In this question, there are 150 values. The values are the number of TV's in each of the 150 houses.

So, the first row of the table tells us that 43 houses have 0 TVs. So, our set of values has 42 zeros.

So far, our set of values looks like this: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, . . . . . }

The second row of the table tells us that 27 houses have 1 TV. So, our set of values has 27 ones.

Now our set of values looks like this: {0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, . . . . . }

And so it goes until we've listed all 150 values, at this point we can locate the two middle values and use them to calculate the median.

Of course, there's a faster way, which is demonstrated in the video.

Does that help?

Cheers,
Brent

Can you elaborate on that approach? It doesn't sound right to me.

Question link:

https://gre.myprepclub.com/forum/qotd-8-internet-use-in-year-x-2505.html

The circle graph tells us that 29% of the world population of internet users are from Europe.
Let T = the TOTAL population of internet users
We can write: 29% of T = number of users from Europe

The chart on the right tells us that there are 27.3 million users from Europe
So, we can write: 29% of T = 27.3 million
Rewrite as: 0.29T = 27.3 million
Solve: T = (27.3 million)/0.29

Does that help?

Cheers,
Brent
PS: I'm glad you like the videos.

I'm not entirely sure what you mean when you write "universe."

Question II asks us to find the mean. So, we add up all 150 values numbers and then divide by 150.

Question III asks us to find the median. So, the solution will be different. Here, we must list the 150 values in ascending order and find the average of the two middlemost values.

So, as we can see, the calculations for mean and median are completely different.

More here: https://www.greenlighttestprep.com/module/gre-statistics/video/800

Does that help?