[latex]\frac{79+86+82+94}{4}=85.25[/latex]. Typically we round means to one more decimal place than the original data had. In this case, we would round 85.25 to 85.3.

Adding these values, we get 634 total TDs. Dividing by 31, the number of data values, we get 634/31 = 20.4516. It would be appropriate to round this to 20.5.

It would be most correct for us to report that “The mean number of touchdown passes thrown in the NFL in the 2000 season was 20.5 passes,” but it is not uncommon to see the more casual word “average” used in place of “mean.”

Calculating the mean by hand could get tricky if we try to type in all 100 values:

[latex]\frac{\overbrace{15+\cdots+15}^{\text{6 terms}}+\overbrace{20+\cdots+20}^{\text{8 terms}}+\overbrace{25+\cdots+25}^{\text{11 terms}}+\cdots}{\text{100}}[/latex]

We could calculate this more easily by noticing that adding 15 to itself six times is the same as 90. Using this simplification, we get

[latex]\frac{15\cdot6+20\cdot8+25\cdot11+30\cdot17+35\cdot19+40\cdot20+45\cdot12+50\cdot7}{\text{100}}=\frac{3390}{100}=33.9[/latex]

The mean household income of our sample is 33.9 thousand dollars or $33,900.

Adding this to our sample, our mean is now:

[latex]\frac{15\cdot6+20\cdot8+25\cdot11+30\cdot17+35\cdot19+40\cdot20+45\cdot12+50\cdot7+5000\cdot1}{\text{101}}=\frac{8390}{101}=83.069[/latex]

The new mean household income of our sample would be 83.069 thousand dollars or $83,069.

Since there are 31 data values, an odd number, the median will be the middle number, the 16th data value (leaving 15 values below and 15 above). The 16th data value is 20, so the median number of touchdown passes in the 2000 season was 20 passes. Notice that for this data, the median is fairly close to the mean we calculated earlier, 20.5.

We start by listing the data in order: 2 4 5 5 6 7 7 8 8 10

Since there are 10 data values, an even number, there is no one middle number. The two middle numbers are 6 and 7.  To find the median, we find the mean of these two middle numbers, and get (6+7)/2 = 6.5.

The median quiz score is 6.5.

Here we have 100 data values. If we didn’t already know that, we could find it by adding the frequencies. Since 100 is an even number, we need to find the mean of the middle two data values – the 50th and 51st data values. To find these, we start counting up from the top:

There are 6 data values of $15, so                  Values 1 to 6 are $15 thousand

The next 8 data values are $20, so                  Values 7 to (6+8)=14 are $20 thousand

The next 11 data values are $25, so                Values 15 to (14+11)=25 are $25 thousand

The next 17 data values are $30, so                Values 26 to (25+17)=42 are $30 thousand

The next 19 data values are $35, so                Values 43 to (42+19)=61 are $35 thousand

From this we can tell that values 50 and 51 will be $35 thousand, and the mean of these two values is $35 thousand. The median income in this neighborhood is $35 thousand.  This is fairly close to our mean which was $33,900.

For this data, Green is the mode, since it is the data value that occurred the most frequently.