AP Stats Summer Assignment Questions

Questions

What is the difference between a quantitative and qualitative variable?

The difference between a quantitative and qualitative variable is that quantitative represents numerrical measurements/counts while qualitatitve represents categories

Categorical is another term for which type of variable?

Categorical is another term for qualitative

Of the “Ways to Display Data above”, which ones are used to display quantitative variables? Which ones are used to display qualitative variables?

Quantitative variables use stem and leaf plots, dot plots, boxplots, scatterplots, and histograms

Qualitative variables use bar graphs and pie charts

What is the 5-number summary of a data set?

Five number summary of a data set is: Minimum, First Quartile (Q1), Median (Q2), Third Quartile (Q3), Maximum

How do you mathematically determine if a data set has an outlier?

To determine if a data set has an outlier you use the 1.5 x IQR Rule
IQR = Q3 - Q1

Lower Fence = Q1 - 1.5 (IQR)

Upper Fence = Q3 + 1.5 (IQR)

Any value below the lower fence or above the upper fence is an outlier

Would the grade distribution of scores on a quiz in an AP class be symmetrical, skewed right or skewed left? Explain.

Grade distribution for scores on a quiz in an AP class would be skewed left as many score high with only a few lower scores

If data is skewed, is it better to describe its center with mean or median? Why?

If data is skewed its better to describe the center with the median because it is resistant to outliers and skewers while the mean is non resistant

If a data set is skewed, is it better to describe its spread with the standard deviation or IQR? Why?

If data set is skewed IQR is better to describe spread because it is resistant while standard deviation is non resistant

Classify each of the following as resistant or non-resistant:

Mean - Non resistant

Median - Resistant

IQR - Resistant

Standard Deviation - Non resistant

Variance - Non resistant

What does it mean to “split stems” when making a stem and leaf plot?

Splitting stems means dividing each stem into 2 or more rows that makes the display easier to read

What is the relationship between variance and standard deviation?

Variance = (Standard Deviation)²

Standard Deviation = Sqrt (Variance)

When would the standard deviation of a data set be zero? When might it be negative?

Standard deviation of a data set is zero when every value is the exact same. Standard deviation is NEVER negative because it is based on squared deviations and is therefore nonnegative