Average From a Table

One concept the SAT throws at you that might be a little foreign is to calculate an average from a table or graph where there are multiple instances of the same value.  

If you are asked to take the average of the following test scores:

Score
87
73
95

Then you would no doubt add up 87+73+95 = 255, and then divide by 3 to get 85.

But what if you were given a table like this?

ScoresNumber of Scores
874
731
952

What this table is telling us is that there were 4 test scores of 87, 1 score of 73, and 2 scores of 95.  To find the average (mean), we have to add up all the scores, and divide by the total number of scores.  So our calculation looks like this:

$$\frac{87+87+87+87+73+95+95}7$$

Strategy:

  1. First, determine if it is a straight average, or if we have a frequency to deal with.  If there’s a frequency, we just multiply each row and write it in a new column out to the right for the total points for that row.
ScoreNumber of ScoresTotal
874348
73173
952190

2. Then add up the second and third columns.

874348
73173
952190
7611

3. Finally, we do our division.  In our example, it is \(\mathbf{611}\div\mathbf7=\mathbf{87}.\mathbf3\)

If there is table with two columns where they ask for the average or mean, it is likely you will need to apply this.

If asked for the median of this data, we need to reorder the numbers so that they are in numerical order by frequency.

This gives us: \(73,\;87,\;87,\;87,\;87,\;95,\;95\)

Now selecting the middle number is easier and we can see that 87 is our median.

histogram is the same type of data as the table above, only in graphical format.

Based on the histogram above, of the following, which is closest to the average (arithmetic mean) number of seeds per apple? 

A) 4
B) 5
C) 6
D) 7

Just as above, we have to figure out our total number of seeds, and total number of apples.  Our equation would be:

$$\frac{3+3+5+5+5+5+6+7+7+9+9+9}{12}=6.1$$

So C) would be our correct answer.