To find out how the mean changes when the number 93 is replaced with 45 in the set of 8 numbers, we first need to calculate the original mean.
Step 1: Calculate the original mean.
The original number in the set is:
- 3430502444611693
Now, we can break it down into specific digits for easier calculation:
- Separate the digits. The original digit length here is just one very large number.
This number can be treated as one entry.
Since we do not have additional entries among the given 8 numbers, let's break down the original entry to see parts:
- Original mean: (3430502444611693) / 1 (because we consider it just one number for simplicity).
The original mean is simply: \[ \text{Mean}_{\text{original}} = 3430502444611693 \]
Step 2: Replace 93 with 45.
Next, we replace the last two digits (93) in the large number with 45:
- New number in the set: 3430502444611645
Step 3: Calculate the new mean.
Now we compute the new mean by dividing the new total by the number of entries:
- New mean: \[ \text{Mean}_{\text{new}} = \frac{3430502444611645}{1} = 3430502444611645 \]
Step 4: Find the change in the mean.
Now let’s calculate the difference between the new mean and original mean:
- Change in mean: \[ \text{Change} = \text{Mean}{\text{new}} - \text{Mean}{\text{original}} = 3430502444611645 - 3430502444611693 = -48 \]
So, the mean decreases by 48 when replacing 93 with 45.
The final result is: \[ \text{The mean change is } -48. \]
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