From the following data, using mean, calculate mean deviation and the coefficient of mean deviation.
15, 17, 19, 25, 30, 35, 48

Answer

To solve the problem of calculating the mean deviation and the coefficient of mean deviation from the given data, we will follow these steps:

### Step 1: Write down the data
The data provided is:
\[ 15, 17, 19, 25, 30, 35, 48 \]

### Step 2: Calculate the Mean
The mean (\( \bar{x} \)) is calculated using the formula:
\[ \bar{x} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

- **Sum of observations**:
\[ 15 + 17 + 19 + 25 + 30 + 35 + 48 = 189 \]

- **Number of observations**:
There are 7 observations.

Now, substituting these values into the mean formula:
\[ \bar{x} = \frac{189}{7} = 27 \]

### Step 3: Calculate the Mean Deviation
Mean deviation (MD) is calculated using the formula:
\[ MD = \frac{\sum |x_i - \bar{x}|}{n} \]
where \( x_i \) are the observations, \( \bar{x} \) is the mean, and \( n \) is the number of observations.

- **Calculate \( |x_i - \bar{x}| \)** for each observation:
\[ |15 - 27| = 12 \]
\[ |17 - 27| = 10 \]
\[ |19 - 27| = 8 \]
\[ |25 - 27| = 2 \]
\[ |30 - 27| = 3 \]
\[ |35 - 27| = 8 \]
\[ |48 - 27| = 21 \]

- **Sum of absolute deviations**:
\[ 12 + 10 + 8 + 2 + 3 + 8 + 21 = 64 \]

- **Mean Deviation**:
\[ MD = \frac{64}{7} \approx 9.14 \]

### Step 4: Calculate the Coefficient of Mean Deviation
The coefficient of mean deviation (CMD) is calculated using the formula:
\[ CMD = \frac{MD}{\bar{x}} \]

Substituting the values we found:
\[ CMD = \frac{9.14}{27} \approx 0.338 \]

### Final Results
- **Mean**: \( 27 \)
- **Mean Deviation**: \( 9.14 \)
- **Coefficient of Mean Deviation**: \( 0.338 \)