Question

Find the mean, median, and mode of the data set: 20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32,

Answer 1

To find the mean, median, and mode of the dataset \(20, 30, 32, 16, 31, 32, 13, 20, 28, 32, 15, 18, 20, 21, 32\), we will follow these steps:

### Step 1: Calculate the Mean

The mean is calculated by taking the sum of all data points and dividing by the number of data points.

1. **Sum of the data points:**
\[
20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 = 20 + 30 + 32 + 16 + 31 + 32 + 13 + 20 + 28 + 32 + 15 + 18 + 20 + 21 + 32 321
\]
2. **Count of data points:**
\[
15 \text{ (there are 15 numbers in the dataset)}
\]

3. **Mean calculation:**
\[
\text{Mean} = \frac{321}{15} \approx 21.4
\]

### Step 2: Calculate the Median

The median is the middle value when the data is ordered from least to greatest.

1. **Ordered dataset:**
\[
13, 15, 16, 18, 20, 20, 20, 21, 28, 30, 31, 32, 32, 32, 32
\]

2. **Finding the median:**
With 15 data points (an odd number), the median is the 8th value in the ordered list.
\[
\text{Median} = 21
\]

### Step 3: Calculate the Mode

The mode is the number that appears most frequently in the dataset.

1. **Count of each number:**
- \(13\) - 1 time
- \(15\) - 1 time
- \(16\) - 1 time
- \(18\) - 1 time
- \(20\) - 3 times
- \(21\) - 1 time
- \(28\) - 1 time
- \(30\) - 1 time
- \(31\) - 1 time
- \(32\) - 5 times

2. **Most frequent value:**
The number \(32\) appears 5 times, which is more than any other number.

### Summary of Results:
- **Mean:** \(21.4\)
- **Median:** \(21\)
- **Mode:** \(32\)