Find the Mode 8 , 8 1/2 , 9 , 9 1/2 , 10 , 10 1/2 , 11

$8$ ,

$8 \frac{1}{2}$ ,

$9$ ,

$9 \frac{1}{2}$ ,

$10$ ,

$10 \frac{1}{2}$ ,

$11$

Step 1

Convert

$8 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$8, 8 + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Add

$8$ and

$\frac{1}{2}$ .

To write

$8$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$8, 8 \cdot \frac{2}{2} + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Combine

$8$ and

$\frac{2}{2}$ .

$8, \frac{8 \cdot 2}{2} + \frac{1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Combine the numerators over the common denominator.

$8, \frac{8 \cdot 2 + 1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Simplify the numerator.

Multiply

$8$ by

$2$ .

$8, \frac{16 + 1}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Add

$16$ and

$1$ .

$8, \frac{17}{2}, 9, 9 \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Step 2

Convert

$9 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$8, \frac{17}{2}, 9, 9 + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Add

$9$ and

$\frac{1}{2}$ .

To write

$9$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$8, \frac{17}{2}, 9, 9 \cdot \frac{2}{2} + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Combine

$9$ and

$\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{9 \cdot 2}{2} + \frac{1}{2}, 10, 10 \frac{1}{2}, 11$

Combine the numerators over the common denominator.

$8, \frac{17}{2}, 9, \frac{9 \cdot 2 + 1}{2}, 10, 10 \frac{1}{2}, 11$

Simplify the numerator.

Multiply

$9$ by

$2$ .

$8, \frac{17}{2}, 9, \frac{18 + 1}{2}, 10, 10 \frac{1}{2}, 11$

Add

$18$ and

$1$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 \frac{1}{2}, 11$

Step 3

Convert

$10 \frac{1}{2}$ to an improper fraction.

A mixed number is an addition of its whole and fractional parts.

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 + \frac{1}{2}, 11$

Add

$10$ and

$\frac{1}{2}$ .

To write

$10$ as a fraction with a common denominator, multiply by

$\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, 10 \cdot \frac{2}{2} + \frac{1}{2}, 11$

Combine

$10$ and

$\frac{2}{2}$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{10 \cdot 2}{2} + \frac{1}{2}, 11$

Combine the numerators over the common denominator.

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{10 \cdot 2 + 1}{2}, 11$

Simplify the numerator.

Multiply

$10$ by

$2$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{20 + 1}{2}, 11$

Add

$20$ and

$1$ .

$8, \frac{17}{2}, 9, \frac{19}{2}, 10, \frac{21}{2}, 11$

Step 4

The mode is the element that occurs most in the data set. In this case, all elements occur only once, so there is no mode.

No mode

Find the Mode 8 , 8 1/2 , 9 , 9 1/2 , 10 , 10 1/2 , 11

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