What is the sum of deviations of the variate values `73, 85, 92, 105, 120 ` from their mean?

Options

A. `-2 `
B. `-1`
C. `0`
D. `5`

Answer

To find the sum of deviations of the variate values \(73, 85, 92, 105, 120\) from their mean, we can follow these steps:

### Step 1: Calculate the Mean
The mean (\(\bar{x}\)) is calculated using the formula:
\[ \bar{x} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]

Here, the observations are \(73, 85, 92, 105, 120\).

First, we find the sum of these observations:
\[ 73 + 85 + 92 + 105 + 120 = 475 \]

Next, we find the number of observations, which is \(5\).

Now, we can calculate the mean:
\[ \bar{x} = \frac{475}{5} = 95 \]

### Step 2: Calculate the Deviations from the Mean
Now, we will calculate the deviations of each observation from the mean:
- For \(x_1 = 73\):
\[ 73 - 95 = -22 \]
- For \(x_2 = 85\):
\[ 85 - 95 = -10 \]
- For \(x_3 = 92\):
\[ 92 - 95 = -3 \]
- For \(x_4 = 105\):
\[ 105 - 95 = 10 \]
- For \(x_5 = 120\):
\[ 120 - 95 = 25 \]

### Step 3: Sum the Deviations
Now, we sum all the deviations:
\[ (-22) + (-10) + (-3) + 10 + 25 \]

Calculating this step by step:
1. \(-22 - 10 = -32\)
2. \(-32 - 3 = -35\)
3. \(-35 + 10 = -25\)
4. \(-25 + 25 = 0\)

Thus, the sum of the deviations is:
\[ \text{Sum of deviations} = 0 \]

### Conclusion
The sum of deviations of the variate values \(73, 85, 92, 105, 120\) from their mean is \(0\).

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