Infer the mean deviation for the following data.
X : 70    65   68    70    75    73     80    70     83    86


To calculate the mean deviation of the given data, we need to follow these steps:

### Step 1: Calculate the Mean (\(\bar{X}\)) of the Data
The mean of the data is the sum of all data points divided by the number of data points.

\[
\bar{X} = \frac{70 + 65 + 68 + 70 + 75 + 73 + 80 + 70 + 83 + 86}{10}
\]

### Step 2: Calculate the Absolute Deviations from the Mean
For each data point \( X_i \), calculate the absolute deviation \( |X_i - \bar{X}| \).

### Step 3: Find the Mean Deviation
The mean deviation is the mean of the absolute deviations calculated in Step 2.

Let’s perform these calculations.

First, let's find the mean.The mean of the data is \( \bar{X} = 74.0 \).

### Step 2: Calculate the Absolute Deviations from the Mean
Now, let's calculate the absolute deviations from the mean and then find the mean deviation.The mean deviation of the data is \( 5.6 \).

Would you like more details on how this was calculated or have any other questions?

Here are 5 related questions for further practice:
1. What is the variance of the given data set?
2. How would the mean deviation change if all values in the data set were increased by 5?
3. Can you calculate the median of the data set?
4. How would the mean deviation be affected if an outlier, such as 100, was added to the data set?
5. How is mean deviation different from standard deviation?

**Tip:** The mean deviation is useful for understanding the average distance of data points from the mean, but it doesn't square the deviations like variance or standard deviation, which reduces the impact of outliers.

Learn how to calculate the mean deviation for a dataset including values like 70, 65, 68, 70, 75, 73, 80, 70, 83, and 86. Understand the steps involved in finding the mean and absolute deviations to determine the average distance of data points from the mean. Suitable for high school students studying statistics.

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