Descriptive Statistics Review

Based on the statistics given in the table is the distribution of Brand A sunflower heights:

• Skewed Left

• Skewed Right

• Roughly Symmetric

• Uniform

• Spread Out

The IQR for Brand A equals:

Answer explanation

You must include units with statistics. "17" in an incomplete answer.

Tags

CCSS.6.SP.B.5C

Which measure of center should be used to compare the distributions?

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

Which measure of spread should be used to compare the distributions?

Answer explanation

Since the distribution of Brand A is skewed, IQR must be used as the measure of spread.

Tags

CCSS.7.SP.B.4

Based on the relative positions of the mean and median for Brand B, which shape would you expect for the distribution?

• Skewed Left

• Skewed Right

• Symmetric

• Uniform

• Normal

Answer explanation

The mean is usually in the direction of the skew

Tags

CCSS.6.SP.B.5D

CCSS.HSS.ID.A.2

What does it mean that Sx = 10.48 cm?

• The spread of the data is 10.48 cm

• A typical sunflower is 10.48 from the median of 236

• A sunflower of Brand B is typically 10.48 cm tall

• A Brand B sunflower's height is typcially 10.48 cm from the mean height of 237 cm

• Brand B sunflower heights will all be within 10.48 cm of the mean height of 237 cm.

Answer explanation

The standard deviation is the typical deviation of an observation relative to the mean.

What percent of Brand A sunflowers are expected to fall between 227 cm and 244 cm?

Answer explanation

The interquartile range (IQR) contains the middle 50% of the data

Tags

CCSS.HSS.ID.A.4

If a Brand B sunflower's height was changed from 225 cm to 234 cm, which of the following would not be changed?  (choose all that apply!)

• Mean

• Median

• Standard Deviation

• IQR

• None of them would be changed

Answer explanation

It increased so the mean increases.

It's closer to the mean, so the standard deviation decreases.  

It's still on the same side of the median, so the median is unchanged.

It moved across the first quartile, so Q1 increased which changes the IQR

When describing a distribution and told to use "SOCS", what 4 attributes must be discussed? (Select all 4 items!)

• Slope

• Center

• Spread

• Outliers

• Shape

Describe the shape of the distribution shown in the boxplot

Answer explanation

The long side of the box is in the direction of the skew