Question

Determine the mean, median and modal values for the set:
(21, 33, 12, 19,31, 16, 25, 18}
(3)
SELECT THE CORRECT ANSWER
mean = 21,875, median = 21, mode = none
mean = 21,875, median = 19, mode = none
mean = 21,875, median = 20, mode = none
None of the given answers

Answer 1

To find the mean, median, and mode for the data set \( \{21, 33, 12, 19, 31, 16, 25, 18\} \), we will perform the calculations as follows:

### Step 1: Calculate the Mean
The mean is calculated by summing all the values in the data set and then dividing by the number of values.

\[
\text{Sum} = 21 + 33 + 12 + 19 + 31 + 16 + 25 + 18 = 175
\]
The number of values in the data set is \( 8 \).

\[
\text{Mean} = \frac{\text{Sum}}{\text{Count}} = \frac{175}{8} = 21.875
\]

### Step 2: Calculate the Median
To find the median, we need to sort the data set in ascending order:

\[
\{12, 16, 18, 19, 21, 25, 31, 33\}
\]

Since there are \( 8 \) values (an even number), the median will be the average of the two middle values (4th and 5th values):

\[
\text{Median} = \frac{19 + 21}{2} = \frac{40}{2} = 20
\]

### Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set. In this case:

\[
\{12, 16, 18, 19, 21, 25, 31, 33\}
\]

Each value appears exactly once, so there is no mode:

\[
\text{Mode} = \text{none}
\]

### Summary of Results
- Mean = 21.875
- Median = 20
- Mode = none

### Selecting the Correct Answer
Based on the calculations, the correct option is:
**mean = 21,875, median = 20, mode = none**.