Multiple choice

In a data of 50 observations, the mean of the first 35 observations is 53 and the last 15 observations is 25. If 5 is added to each of the first 35 observations and 3 is subtracted from each of the last 15 observations, then what is the mean of the 50 observations altogether?

  1. 47.2

  2. 45

  3. 40

  4. 39.5

  5. None of these.
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A Correct answer
Explanation

Original sum = 35 * 53 + 15 * 25 = 1855 + 375 = 2230. Total change = 35 * 5 - 15 * 3 = 175 - 45 = 130. New sum = 2230 + 130 = 2360. New mean = 2360 / 50 = 47.2.

AI explanation

The total sum of the first 35 observations is 35 multiplied by 53, which equals 1855, and adding 5 to each increases this sum by 175 to become 2030. The total sum of the last 15 observations is 15 multiplied by 25, which equals 375, and subtracting 3 from each decreases this sum by 45 to become 330. The new mean is the sum of all modified observations divided by 50, calculated as (2030 + 330) divided by 50, resulting in 2360 divided by 50, which equals 47.2.

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