Question

What is the mean, median and mode of the following data?<div>14, 22, 18, 12, 14, 8, 4, 12, 32, 12</div>

mean = 14.8, median = 13, mode = 12

mean = 13, median = 14.8, mode = 12

mean = 13, median = 12, mode = 14.8

mean = 12, median = 14.8, mode = 13

Answer 1

To find the mean, median, and mode of the data set \(14, 22, 18, 12, 14, 8, 4, 12, 32, 12\), we will calculate each one step by step.

1. **Mean**:
The mean is calculated by adding all the numbers together and dividing by the total number of values.

\[
\text{Mean} = \frac{(14 + 22 + 18 + 12 + 14 + 8 + 4 + 12 + 32 + 12)}{10}
\]
\[
= \frac{(14 + 22 + 18 + 12 + 14 + 8 + 4 + 12 + 32 + 12)}{10} = \frac{(14 + 22 + 18 + 12 + 14 + 8 + 4 + 12 + 32 + 12)}{10} = \frac{ 14 + 22 + 18 + 12 + 14 + 8 + 4 + 12 + 32 + 12} {10} = \frac{ 18 2 + 4+4 + 18 + 32 + 12 }{10}
\]
\[
= \frac{ 14 + 18+8 + 32 + 12 }{10}
\]
\[
= \frac{ 11 }{10} = 14.8
\]

2. **Median**:
To find the median, we first need to sort the values in ascending order:
\(4, 8, 12, 12, 12, 14, 14, 18, 22, 32\).

Since there are 10 values (an even number), the median is the average of the 5th and 6th values:
\[
\text{Median} = \frac{12 + 14}{2} = \frac{26}{2} = 13
\]

3. **Mode**:
The mode is the number that appears most frequently. In this dataset, the number 12 appears three times, which is more than any other number.
\[
\text{Mode} = 12
\]

Thus, we have:
- Mean = 14.8
- Median = 13
- Mode = 12

So the correct answer is:

**mean = 14.8, median = 13, mode = 12.**