Question

Here are the prices of five new pairs of hockey skates, in dollars: 59, 60, 65, 99, 175. The standard deviation is about $49. If a sixth pair of skates is added to the data that has a price of $450, what happens to the standard deviation?

Answer 1

Answer:"The new standard deviation is greater than $49"

Explanation:

I did the test and got it correct

Answer 2

The standard deviation of the new data will be increased as compared to the previous standard deviation of the data.

Explanation:

The prices are given to be : 59, 60, 65, 99, 175

Standard deviation = $49

Now, if we add or subtract any constant value to each of the terms then the standard deviation remains unchanged.

But, we add a new price in the given data that is $450

`\text{New standard deviation = }\sqrt{\frac{\sum (\bar{x}-x_i)^2}{n}}\\\\\bar{x}\text{ is the mean of data after adding 450 and}\\x_i\text{ are the price values of the sample data}`

Hence, Standard deviation is calculated to be 139.5

Therefore, the standard deviation of the new data will be increased as compared to the previous standard deviation of the data.