Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if each of the observations, given above, be decreased by `40%`.

Answer

To find the mean of the given numbers and the resulting mean after decreasing each observation by 40%, we can follow these steps:

### Step 1: Calculate the Mean of the Original Data
1. **List the observations**: 8, 12, 16, 22, 10, 4.
2. **Sum the observations**:
\[ 8 + 12 + 16 + 22 + 10 + 4 = 72 \]
3. **Count the number of observations**: There are 6 observations.
4. **Calculate the mean**:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{72}{6} = 12 \]

### Step 2: Calculate the Resulting Mean After Decreasing Each Observation by 40%
1. **Determine the decrease**:
- Calculate 40% of the mean:
\[ 40\% \text{ of } 12 = \frac{40}{100} \times 12 = 4.8 \]
2. **Calculate the resulting mean**:
\[ \text{Resulting Mean} = \text{Original Mean} - 40\% \text{ of Original Mean} = 12 - 4.8 = 7.2 \]

### Final Answer
The mean of the original data is **12**, and the resulting mean after decreasing each observation by 40% is **7.2**.

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