MYP Extended Mathematics 8 Variation and Standard Deviation Questionbank

On a box-and-whisker plot, if the central box is very narrow (representing a small interquartile range) compared to the total length of the whiskers (representing a large range), what does this specifically indicate about the data distribution?

In Data Set ${A}$, the population standard deviation is small (${ ext{\sigma} = 2 }$), while in Data Set ${B}$, it is large (${ ext{\sigma} = 10 }$). If both sets share a mean of ${ 50 }$, in which set is the mean a more representative "typical" value?

3

1

4

2

$\sqrt{18}$

6

$\sqrt{9}$

The data points become more spread out from the mean, and the standard deviation increases.

The data points become more tightly clustered around the mean, and the standard deviation decreases.

The standard deviation remains $10\text{ minutes}$ because the mean commute time of the group has not changed.

The standard deviation increases because the total number of data points has increased.

3