The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is
Question
The mean of 25 observations is 36. Out of these observations if the mean of first 13 observations is 32 and that of the last 13 observations is 40, the 13th observation is
Solution
Step 1: Calculate the total sum of all 25 observations.
The mean of 25 observations is 36. The mean is calculated by dividing the total sum of the observations by the number of observations. So, the total sum of all 25 observations is 36 * 25 = 900.
Step 2: Calculate the total sum of the first 13 observations.
The mean of the first 13 observations is 32. So, the total sum of the first 13 observations is 32 * 13 = 416.
Step 3: Calculate the total sum of the last 13 observations.
The mean of the last 13 observations is 40. So, the total sum of the last 13 observations is 40 * 13 = 520.
Step 4: Calculate the 13th observation.
The 13th observation is included in both the first 13 observations and the last 13 observations. So, to find the 13th observation, we add the total sum of the first 13 observations and the total sum of the last 13 observations, and then subtract the total sum of all 25 observations.
So, the 13th observation is 416 + 520 - 900 = 36.
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