A data consist of 50 positive values, and the mean of the data is m. A new data set is made by increasing each value in the original data set by 8. Which of the following represents the mean by the new data set in terms of m ?
Question
A data consist of 50 positive values, and the mean of the data is m. A new data set is made by increasing each value in the original data set by 8. Which of the following represents the mean by the new data set in terms of m ?
Solution
The mean of a data set is calculated by summing all the values in the set and then dividing by the number of values.
In the original data set, the mean is given as m. This means that the sum of all the values in the set is 50m (because there are 50 values).
When each value in the set is increased by 8, the total increase in the sum of the values is 8*50 = 400 (because each of the 50 values increases by 8).
So, the sum of the values in the new data set is 50m + 400.
The mean of the new data set is therefore (50m + 400) / 50 = m + 8.
So, the mean of the new data set in terms of m is m + 8.
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