The mean of 25 numbers is 36. If the mean of the first thirteen numbers is 32 and that of the last 13 numbers is 39, find the 13th number.
Question
The mean of 25 numbers is 36. If the mean of the first thirteen numbers is 32 and that of the last 13 numbers is 39, find the 13th number.
Solution
Sure, let's solve this step by step:
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The mean of 25 numbers is 36. This means the total sum of these 25 numbers is 25*36 = 900.
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The mean of the first 13 numbers is 32. This means the total sum of these 13 numbers is 13*32 = 416.
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The mean of the last 13 numbers is 39. This means the total sum of these 13 numbers is 13*39 = 507.
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The 13th number is included in both the first 13 numbers and the last 13 numbers. So, if we add the sum of the first 13 numbers and the sum of the last 13 numbers, we have counted the 13th number twice.
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Therefore, the sum of the first 13 numbers and the last 13 numbers is 416 + 507 = 923.
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Since we have counted the 13th number twice, we subtract the total sum of the 25 numbers from this result to find the 13th number: 923 - 900 = 23.
So, the 13th number is 23.
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