Question

The mean of a data set is equal to $10$ and its standard deviation is equal to $1$. If we add $5$ to each data value, then what will happen to the mean and standard deviation of the new data.

Answer 1

Hint: According to given in the question we have to determine what will happen to the mean and standard deviation of the new data when the mean of a data set is equal to $10$ and its standard deviation is equal to $1$ and if we add $5$to each data value. So, first of all we have to understand about the mean which is as explained below:
Mean: The mean of the data set can be determined by adding all the numbers in the data set and dividing by the number of values in the set. Where, the median is the middle value when the given data set is arranged in the ascending order.
Now, we have to understand about the standard deviation which is as explained below:
Standard deviation: Standard deviation is the measure of dispersion of a set of data from its mean and its mean is the absolute variability of a distribution.
Now, as mentioned in the question that $5$ is added to all of the data then the mean will also be increased and then we have to check for the standard deviation.

Complete step-by-step solution:
Step 1: First of all as mentioned in the question that 5 is added to the all of the data then the mean will also be increased as mentioned in the solution hint. Hence, each given data will be increased by $5$.
Step 2: Now, from step 1 we can say that the mean of the given data will increase.
Step 3: Now, as we know that standard deviation is the measure of dispersion of a set of data from its mean and its mean is the absolute variability of a distribution. Which measure the distance between the mean and the data values will not change.

Hence, The mean will also increase by $5$ and the standard deviation will remain the same as it is.

Note: The greater is the standard deviation and grater will be the magnitude of the deviation of the value from their mean.
The mean of the data set can be determined by adding all the numbers in the data set and dividing by the number of values in the set.