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The mean of 100 observations was calculated as 69. It was found later on that one of the observations was misread as 92 instead of 67. The correct mean is: Options :69.2568.2567.75none of these

Question

The mean of 100 observations was calculated as 69. It was found later on that one of the observations was misread as 92 instead of 67. The correct mean is: Options :69.2568.2567.75none of these

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Solution 1

The correct mean can be calculated using the following steps:

  1. First, calculate the total sum of the 100 observations. Since the mean was initially calculated as 69, the total sum would be 69 * 100 = 6900.

  2. Then, subtract the incorrect observation from the total sum. The incorrect observation was 92, so the corrected total sum would be 6900 - 92 = 6808.

  3. Add the correct observation to the corrected total sum. The correct observation was 67, so the final total sum would be 6808 + 67 = 6875.

  4. Finally, calculate the correct mean by dividing the final total sum by the total number of observations. The correct mean would be 6875 / 100 = 68.75.

So, the correct mean is 68.75.

This problem has been solved

Solution 2

The correct mean can be calculated by following these steps:

  1. First, calculate the total sum of the 100 observations. Since the mean was initially calculated as 69, the total sum would be 69 * 100 = 6900.

  2. Then, subtract the incorrect observation from the total sum. The incorrect observation was 92, so the corrected total sum would be 6900 - 92 = 6808.

  3. Add the correct observation to the corrected total sum. The correct observation was 67, so the final total sum would be 6808 + 67 = 6875.

  4. Finally, calculate the correct mean by dividing the final total sum by the number of observations. The correct mean would be 6875 / 100 = 68.75.

So, the correct mean is 68.75.

This problem has been solved

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