Question

The distribution of the prices of new phone is positively skewed with a long tail to the right, in a random sample of people who have purchased a new phone, a mean and standard deviation price of a new phone is reported to be $400 and $50 respectively.

What is the standard deviation of price of a new phone costing $500 in this distribution? Please indicate the standard deviation with the sign (negative and positive) and in the unit as “s”

Answer 1

The distribution of the prices of a new phone is positively skewed with a long tail to the right, in a random sample of people who have purchased a new phone, a mean and standard deviation price of a new phone is reported to be $400 and $50 respectively.

We have to find the standard deviation of the price of a new phone costing $500 in this distribution.

The sign of the standard deviation is always positive. The standard deviation cannot be negative because it is square rooted variance. Let me explain this:
Variance is calculated by summing all the squared distances from the mean and dividing them by the number of all cases. So if one data entry in calculating variance is negative, it will always become positive when squared.
And finally, when we square root the variance to get the standard deviation, it must be a positive number because the square root of a positive number is always a positive number.

Here Standard deviation will be the same. So the standard deviation of the price of a new phone costing $500 in this distribution is $50.

Thanks and regards.