(ii)Find the mean deviation of numbers 3,4,5,6,7 from mean.

Answer

To find the mean deviation of the numbers 3, 4, 5, 6, and 7 from their mean, we can follow these steps:

### Step 1: Calculate the Mean
First, we need to find the mean (average) of the given numbers.

Given numbers: 3, 4, 5, 6, 7

Mean \( \bar{x} \) is calculated as:
\[ \bar{x} = \frac{\text{Sum of all observations}}{\text{Number of observations}} \]

Calculating the sum:
\[ 3 + 4 + 5 + 6 + 7 = 25 \]

Number of observations \( n = 5 \).

Now, substituting the values into the mean formula:
\[ \bar{x} = \frac{25}{5} = 5 \]

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

The deviations are:
\[ |3 - 5|, |4 - 5|, |5 - 5|, |6 - 5|, |7 - 5| \]

Calculating each deviation:
- \( |3 - 5| = | -2 | = 2 \)
- \( |4 - 5| = | -1 | = 1 \)
- \( |5 - 5| = | 0 | = 0 \)
- \( |6 - 5| = | 1 | = 1 \)
- \( |7 - 5| = | 2 | = 2 \)

### Step 3: Sum of the Absolute Deviations
Now, we sum all the absolute deviations:
\[ 2 + 1 + 0 + 1 + 2 = 6 \]

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

Mean Deviation \( D \) is given by:
\[ D = \frac{\text{Sum of absolute deviations}}{n} \]
Substituting the values:
\[ D = \frac{6}{5} = 1.2 \]

### Final Answer
The mean deviation of the numbers 3, 4, 5, 6, and 7 from their mean is **1.2**.

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