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SAT II Math I : Mode

Study concepts, example questions & explanations for SAT II Math I

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Example Questions

Example Question #1 : Mode

Find the mode of the following set of numbers:

$\displaystyle 5,3,2,3,3,7,9,2$

Possible Answers:

$\displaystyle 5$

$\displaystyle 3$

$\displaystyle 2$

$\displaystyle 9$

$\displaystyle 7$

Correct answer:

$\displaystyle 3$

Explanation:

The mode of a set of numbers is the one that appears most often. Thus, our answer is $\displaystyle 3$.

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Example Question #2 : Mode

Find the mode of the following set of numbers:

$\displaystyle 4,1,-2,5,1,8,9$

Possible Answers:

$\displaystyle 1$

$\displaystyle 9$

$\displaystyle 4$

$\displaystyle -1$

$\displaystyle 2$

Correct answer:

$\displaystyle 1$

Explanation:

The mode is the number that occurs the most frequently, so our answer is $\displaystyle 1$.

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Example Question #3 : Mode

What is the mode of 8, 7, 5, 4, 12, 13, 7, 2, 7?

Possible Answers:

$\displaystyle 4$

$\displaystyle 7$

$\displaystyle 12$

$\displaystyle 8$

Correct answer:

$\displaystyle 7$

Explanation:

The mode is the number that is repeated the most within a set. In our case we see 7 repeated 3 times therefore our mode is 7

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Example Question #4 : Mode

What's the mode?

$\displaystyle 23, 24, 26, 25, 27, 23, 28, 29, 25, 21$

Possible Answers:

23, 25 $\displaystyle 23, 25$

$\displaystyle 28$

$\displaystyle 27$

$\displaystyle 25$

$\displaystyle 23$

Correct answer:

23, 25 $\displaystyle 23, 25$

Explanation:

Mode is the number occuring the most in the data set. By rearrangging in increasing order, we see that $\displaystyle 23$ and $\displaystyle 25$ occur twice. That will be our answers.

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Example Question #5 : Mode

$\left \{ 1,1,1,1,1,2,3,4,5,6,7,7,7\right \}$ $\displaystyle \left \{ 1,1,1,1,1,2,3,4,5,6,7,7,7\right \}$

Which value above would be the mode of this particular data set?

Possible Answers:

$\displaystyle 3$

$\displaystyle 1$

3.5 $\displaystyle 3.5$

$\displaystyle 7$

$\displaystyle 4$

Correct answer:

$\displaystyle 1$

Explanation:

The mode is the value that occurs the most times in one set. In the given set that value is $\displaystyle 1$ which occurs five times.

$\left \{ {\color{Red} 1,1,1,1,1},2,3,4,5,6,7,7,7\right \}$ $\displaystyle \left \{ {\color{Red} 1,1,1,1,1},2,3,4,5,6,7,7,7\right \}$

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Example Question #5 : Mode

A class of statistics students scored the following on their last test:$\displaystyle 98, 65, 85, 100, 76, 50, 88, 63, 70, 65, 70, 99, 82, 80, 78, 65, 94, 66$.

Calculate the mode for this data set.

Possible Answers:

$\displaystyle 65$

$\displaystyle 70$

$\displaystyle 87$

$\displaystyle 80$

$\displaystyle 64$

Correct answer:

$\displaystyle 65$

Explanation:

The mode is the number that shows up more often than the others in a set of data.

If we put our data set in order we see:

98, 65, 85, 100, 76, 50, 88, 63, 70, 65, 70, 99, 82, 80, 78, 65, 94, 66

Becomes,

50, 63, 65, 65, 65, 66, 70, 70, 76, 78, 80, 82, 85, 88, 94, 98, 99, 100.

Therefore, 65 is the mode because it appears 3 times.

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Example Question #1 : Mode

What is the mode of the following data set?

{9, 10, 4, 11, 7, 5, 15, 7, 2, 20, 11, 19, 7, 9}

Possible Answers:

7 and 9

Correct answer:

Explanation:

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.

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Example Question #4 : How To Find Mode

A set comprises ten elements, which are

$\begin{Bmatrix} 10, 12, 18, 12, 19, 20, 12, 19, 11, N \end{Bmatrix}$ $\displaystyle \begin{Bmatrix} 10, 12, 18, 12, 19, 20, 12, 19, 11, N \end{Bmatrix}$

where $\displaystyle N$ stands for an unknown number.

What can $\displaystyle N$ be set to in order to make the set bimodal?

Possible Answers:

$\displaystyle 10$

$\displaystyle 12$

The set cannot be bimodal for any value of N.

$\displaystyle 19$

$\displaystyle 11$

Correct answer:

$\displaystyle 19$

Explanation:

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.

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Example Question #6 : Mode

Find the mode of the set:

$\displaystyle 7, 10, 16, 16, 16, 16, 17, 23, 25, 27, 30, 31, 41, 57, 57, 58$

Possible Answers:

$\displaystyle 23$

$\displaystyle 17$

$\displaystyle 16$

$\displaystyle 57$

Correct answer:

$\displaystyle 16$

Explanation:

The mode is the most repeated number in the set. To answer this, find the number that occurs the most number of times in the set.

$7, 10, {\color{Red} 16}, {\color{Red} 16}, {\color{Red} 16}, {\color{Red} 16}, 17, 23, 25, 27, 30, 31, 41, 57, 57, 58$ $\displaystyle 7, 10, {\color{Red} 16}, {\color{Red} 16}, {\color{Red} 16}, {\color{Red} 16}, 17, 23, 25, 27, 30, 31, 41, 57, 57, 58$

For this problem that gives us the answer of 16 for the mode.

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Example Question #7 : Mode

Find the mode of the set:

$\displaystyle 11, 13, 17, 22, 22, 22, 23, 23, 26, 28, 47, 49$

Possible Answers:

$\displaystyle 23$

$\displaystyle 17$

$\displaystyle 26$

$\displaystyle 22$

Correct answer:

$\displaystyle 22$

Explanation:

The mode is the most repeated number in the set. To answer this, find the number that occurs the most number of times in the set.

$11, 13, 17,{\color{Red} 22}, {\color{Red} 22}, {\color{Red} 22}, 23, 23, 26, 28, 47, 49$ $\displaystyle 11, 13, 17,{\color{Red} 22}, {\color{Red} 22}, {\color{Red} 22}, 23, 23, 26, 28, 47, 49$

For this problem that gives us the answer of 22 for the mode.

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SAT II Math I : Mode

Study concepts, example questions & explanations for SAT II Math I

All SAT II Math I Resources

Example Questions

Example Question #1 : Mode

Example Question #2 : Mode

Example Question #3 : Mode

Example Question #4 : Mode

Example Question #5 : Mode

Example Question #5 : Mode

Example Question #1 : Mode

Example Question #4 : How To Find Mode

Example Question #6 : Mode

Example Question #7 : Mode

All SAT II Math I Resources

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