Find the mean deviation from the mean of the following discrete data 6,7, 10,1213,4,12 ,16

Answer

To find the mean deviation from the mean of the given discrete data: 6, 7, 10, 12, 13, 4, and 16, we will follow these steps:

### Step 1: Calculate the Mean
The mean (average) of the data set is calculated using the formula:

\[ \text{Mean} ( \bar{x} ) = \frac{\sum x_i}{n} \]

Where \( x_i \) are the data points and \( n \) is the number of data points.

Given data: 6, 7, 10, 12, 13, 4, 16

Calculating the sum:

\[ \sum x_i = 6 + 7 + 10 + 12 + 13 + 4 + 16 = 68 \]

The number of data points \( n = 7 \).

Now, substituting into the mean formula:

\[ \bar{x} = \frac{68}{7} \approx 9.71 \]

### Step 2: Calculate the Absolute Deviations
Next, we find the absolute deviations from the mean for each data point:

\[ |x_i - \bar{x}| \]

Calculating each deviation:

- For 6: \( |6 - 9.71| \approx 3.71 \)
- For 7: \( |7 - 9.71| \approx 2.71 \)
- For 10: \( |10 - 9.71| \approx 0.29 \)
- For 12: \( |12 - 9.71| \approx 2.29 \)
- For 13: \( |13 - 9.71| \approx 3.29 \)
- For 4: \( |4 - 9.71| \approx 5.71 \)
- For 16: \( |16 - 9.71| \approx 6.29 \)

### Step 3: Sum of Absolute Deviations
Now, we sum these absolute deviations:

\[ \text{Sum of absolute deviations} = 3.71 + 2.71 + 0.29 + 2.29 + 3.29 + 5.71 + 6.29 = 24.29 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation using the formula:

\[ \text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{n} \]

Substituting the values:

\[ \text{Mean Deviation} = \frac{24.29}{7} \approx 3.47 \]

### Final Answer
The mean deviation from the mean of the given data is approximately **3.47**.

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