Text +Quiz: What Measures of Spread & Center Should We Use?

More On Center And Spread

When analyzing skewed data, it is common to report numeric summaries like the median and 5 number summary, as the mean and standard deviation may be misleading.

However, with symmetric data, the mean and standard deviation are commonly used, as we can understand what proportion of points might fall 1, 2, or 3 standard deviations away based on the empirical rule associated with normal distributions.

You can read more about this here.

Standard Deviation and Skewed Distributions

Standard Deviations can be calculated for any data set, whether it is normally distributed or skewed. So with the data below be careful what assumptions you are making about the underlying data.

Also the standard deviation basically provides which of two sets of data are more spread out.

If we know the following about heights for the accountants in our company and the IT people in our company:

The mean height of accountants is 67.84 in.
The mean height of IT staff is 69.76 in.
The standard deviation of heights for accountants is 4.5 in.
The standard deviation of heights for IT staff is 3.2 in.

Which of the below statements are definitely true? Select all that apply.

All accountants are taller than all IT staff.

On average, accountants are shorter than IT staff.

There is more variability in the heights of the accountants than the heights of the IT staff.

There is less variability in the heights of the accountants than the heights of the IT staff.

The distribution of heights for accountants is normally distributed.

SOLUTION:

On average, accountants are shorter than IT staff.
There is more variability in the heights of the accountants than the heights of the IT staff.