Find the mean deviation of the following: 170,190,180,40,30,50,200,150,110,20

To calculate the **mean deviation** of a set of values, follow these steps:

1. **Find the mean** (average) of the data.
2. **Calculate the absolute deviations** from the mean for each value.
3. **Find the mean of those absolute deviations**.

### Step 1: Find the Mean

The mean (\(\bar{x}\)) is the sum of all values divided by the number of values.

Given dataTo calculate the **mean deviation** of a set of values, follow these steps:

1. **Find the mean** (average) of the data.
2. **Calculate the absolute deviations** from the mean for each value.
3. **Find the mean of those absolute deviations**.

### Step 1: Find the Mean

The mean (\(\bar{x}\)) is the sum of all values divided by the number of values.

Given  170, 190, 180, 40, 30, 50, 200, 150, 110, 20

\[
\bar{x} = \frac{170 + 190 + 180 + 40 + 30 + 50 + 200 + 150 + 110 + 20}{10}
\]

\[
\bar{x} = \frac{1140}{10} = 114
\]

### Step 2: Calculate the Absolute Deviations from the Mean

Next, subtract the mean from each value and take the absolute value of the result:

\[
|170 - 114| = 56
\]
\[
|190 - 114| = 76
\]
\[
|180 - 114| = 66
\]
\[
|40 - 114| = 74
\]
\[
|30 - 114| = 84
\]
\[
|50 - 114| = 64
\]
\[
|200 - 114| = 86
\]
\[
|150 - 114| = 36
\]
\[
|110 - 114| = 4
\]
\[
|20 - 114| = 94
\]

### Step 3: Find the Mean of the Absolute Deviations

Now, sum the absolute deviations and divide by the number of values:

\[
\text{Mean Deviation} = \frac{56 + 76 + 66 + 74 + 84 + 64 + 86 + 36 + 4 + 94}{10}
\]

\[
\text{Mean Deviation} = \frac{640}{10} = 64
\]

### Final Answer:
The **mean deviation** is **64**.

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. How do you calculate the standard deviation of a dataset?
2. What is the difference between mean deviation and standard deviation?
3. How is variance related to standard deviation?
4. Calculate the mean deviation of the set: 25, 30, 35, 40, 45.
5. How does the median affect the calculation of mean deviation?

**Tip**: Mean deviation is useful when you want to understand how spread out the values are from the mean in a simple, non-squared manner.

Learn how to calculate the mean deviation for the dataset 170, 190, 180, 40, 30, 50, 200, 150, 110, 20 with a detailed step-by-step solution. This problem covers essential statistical concepts, including mean calculation and absolute deviation. Suitable for students in Grades 8-10.

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