when tested the lives (in hours) of 5 bulbs were noted as follows 1357,1090,1666,1494,1623
The mean deviations (in hours ) from their mean is

Options

A. 178
B. 179
C. 220
D. 356

Explanation

To find the mean deviation from the mean for the lives of the 5 bulbs (1357, 1090, 1666, 1494, 1623), we will follow these steps:

### Step 1: Calculate the Mean (x̄)
To find the mean, we sum all the values and divide by the number of observations.

\[ x̄ = \frac{\text{Sum of all values}}{n} \]

Where:
- Sum of all values = 1357 + 1090 + 1666 + 1494 + 1623
- n = 5 (the number of bulbs)

Calculating the sum:
\[ 1357 + 1090 + 1666 + 1494 + 1623 = 7230 \]

Now, calculate the mean:
\[ x̄ = \frac{7230}{5} = 1446 \]

### Step 2: Calculate the Deviations from the Mean
Next, we calculate the absolute deviations of each value from the mean.

\[ d_i = |x_i - x̄| \]

Where \(x_i\) are the individual bulb lives:
- For 1357: \(d_1 = |1357 - 1446| = | -89 | = 89\)
- For 1090: \(d_2 = |1090 - 1446| = | -356 | = 356\)
- For 1666: \(d_3 = |1666 - 1446| = | 220 | = 220\)
- For 1494: \(d_4 = |1494 - 1446| = | 48 | = 48\)
- For 1623: \(d_5 = |1623 - 1446| = | 177 | = 177\)

### Step 3: Sum the Absolute Deviations
Now we sum all the absolute deviations:
\[ \text{Sum of deviations} = d_1 + d_2 + d_3 + d_4 + d_5 = 89 + 356 + 220 + 48 + 177 \]

Calculating the sum:
\[ 89 + 356 + 220 + 48 + 177 = 890 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation by dividing the sum of deviations by the number of observations.

\[ \text{Mean Deviation} = \frac{\text{Sum of deviations}}{n} = \frac{890}{5} = 178 \]

### Final Answer
The mean deviation from their mean is **178 hours**.

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