The mean deviation from mean of the data 90,100,125,115,110 is

Options

A. 10
B. 10.4
C. 10.6
D. 10.8

Answer

To find the mean deviation from the mean of the data set \(90, 100, 125, 115, 110\), we will follow these steps:

### Step 1: Calculate the Mean
The mean (\( \bar{x} \)) is calculated using the formula:

\[ \bar{x} = \frac{\sum x_i}{n} \]

Where \( \sum x_i \) is the sum of all data points, and \( n \) is the number of data points.

**Calculation:**
\[ \sum x_i = 90 + 100 + 125 + 115 + 110 = 540 \]
\[ n = 5 \]
\[ \bar{x} = \frac{540}{5} = 108 \]

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

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

**Calculations:**
- For \( x_1 = 90 \):
\[ |90 - 108| = | -18 | = 18 \]
- For \( x_2 = 100 \):
\[ |100 - 108| = | -8 | = 8 \]
- For \( x_3 = 125 \):
\[ |125 - 108| = | 17 | = 17 \]
- For \( x_4 = 115 \):
\[ |115 - 108| = | 7 | = 7 \]
- For \( x_5 = 110 \):
\[ |110 - 108| = | 2 | = 2 \]

### Step 3: Sum the Absolute Deviations
Now, we sum all the absolute deviations calculated in Step 2:

\[ \text{Sum of absolute deviations} = 18 + 8 + 17 + 7 + 2 = 52 \]

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

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

**Calculation:**
\[ \text{Mean Deviation} = \frac{52}{5} = 10.4 \]

### Conclusion
The mean deviation from the mean of the data \(90, 100, 125, 115, 110\) is \(10.4\).

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