When rolling two six-sided dice there are \(\displaystyle 36\) possible outcomes.

\(\displaystyle 6\ \textup{outcomes of die 1}*6\ \textup{outcomes of die 2}=36\ \textup{possible outcomes}\)

The possible combinations to get a seven are: \(\displaystyle 1,6\; \; \; 2,5\; \; \; 3,4\; \; \; 4,3\; \; \; 5,2\; \; \; 6,1\).

So there are six ways to get a seven, out of \(\displaystyle 36\) combinations total. The resulting probability of getting a seven is \(\displaystyle \frac{6}{36}= \frac{1}{6}\).

The probability of NOT getting a seven is \(\displaystyle 1-\frac{1}{6}= \frac{5}{6}\).

The mode is the value that appears most often in a set of data. Within the class, 7 students answered 5 questions correctly, 12 students answered 4 questions correctly, 9 students answered 3 questions correctly, and 2 students answered 2 questions correctly. More students scored a 4 than any other score, so this score is the class's mode.

\(\displaystyle \{ 3, 7, 8, 9, 10, 10, 10, 10, 11, 11, 13, N \}\) is the correct set; no matter what \(\displaystyle N\) is, no value other than 10 can appear four or more times.

To see that no other choice works, let's examine them.

\(\displaystyle \{ 7, 8, 9, 10, 10, 11, 11, 13, N \}\): If \(\displaystyle N\) is any number other than 10 or 11, then the number has 10 and 11, and possibly one other number, as modes, each appearing twice.

\(\displaystyle \{ 1, 2, 3, 4, 5, 6, 7, 8, 9, N \}\) : If \(\displaystyle N\) is not any of the numbers already in the set, the set has no repeated values and thus no mode.

\(\displaystyle \{ 8, 8, 8, N, N, N \}\): If \(\displaystyle N \neq 8\), then the set is bimodal, with 8 and \(\displaystyle N\) the modes.

\(\displaystyle \{ 9, 10, 10, 10, 10, 11, 11, 13, N, N \}\) : If \(\displaystyle N = 11\), the set is bimodal, with 10 and 11 the modes.

The mode of a set of numbers is the number that appears the most.  In this set of numbers, 2 appears twice, and all of the other numbers appear only once.  Thus, 2 is the mode of this set of numbers.

The mode of a set of statistics is simply the most commonly occuring observation. In this case, what was the most common score on the quiz? We have 5 instances of 81, which is the most occurences of any particular number, thus our mode is 81.

\(\displaystyle A = \begin{Bmatrix}0, 5, 6, 4, -1, 0, 5, 4, -5, 1\end{Bmatrix}\)

Mode refers to the number occuring most often, so in this example we are looking for the numbers that repeat and how many times they repeat. 

\(\displaystyle 0\) repeats twice

\(\displaystyle 4\) repeats twice

\(\displaystyle 5\) repeats twice 

Now because all three numbers repeated an equal amount of time, all three then become our mode. 

Answer : \(\displaystyle \begin{Bmatrix} 0 , 5 , 4\end{Bmatrix}\)

The mode is the number that appears the most in the number set. To figure out what number appears the most in our number set, it would help to rearrange the numbers so that the set is rewritten as

9, 10, 12, 12, 12, 14, 14, 15, 16, 17, 17, 17, 17, 18, 19

By looking at this number set, it seems that the number 17 is the most common number in the number set.  It appears 4 times while other numbers such as 12 appear three times.  Thus, 17 is the mode.

There are 12 total pens (4 + 3 + 5 = 12). There 3 blue pens of the 12 total. The chances of grabbing a blue pen are \(\displaystyle \frac{3}{12}\), which reduces to \(\displaystyle \frac{1}{4}\).

Arrange the set in numerical order: {2, 4, 5, 7, 7, 7, 9, 9, 10, 11, 11, 15, 19, 20}.

You can then chart the frequency of each value.

Value (Frequency)

2 (1)

4 (1)

5 (1)

7 (3)

9 (2)

10 (1)

11 (2)

15 (1)

19 (1)

20 (1)

From this you can see the most common value, which is the mode, is 7.

12 appears in the set most frequently, appearing three times; 19 is second in frequency, appearing twice. 10, 11, 18, and 20 appear once each.

The only number we can set \(\displaystyle N\) to to make two data values tie for appearing most frequently is 19; 12 and 19 would then each appear three times, and the others, once. If \(\displaystyle N\) is set to any other number, 12 would remain the most frequent data value.