AP Stats Unit 1 Verbal Exam

In statistics, what is meant by individuals?

Individuals are the group where data is collected from.

In statistics, what is meant by a variable?

Any attribute that can differ from individual to individual

What is the difference between a categorical variable and a quantitative variable?

Categorical variables can be assigned to categories based on labels, while quantitative data is expressed in numbers.

When is it useful to use a bar chart?

Bar charts are helpful for depicting frequency (aka the number of times a value appears in a dataset)

When is it useful to use a pie chart?

Pie charts are helpful for depicting relative frequency (aka the frequency divided by the total number of data points)

What is meant by a distribution?

A distribution is the set of values observed from a measurement or variables

Define range:

Range is the difference between the maximum and minimum values in a dataset.

When is it better to use a histogram rather than a dot plot?

Histograms are better to use than dot plots when there’s a larger data set

What is meant by frequency in a histogram?

Frequency in a histogram tells how many occurrences happen within each bar

Define outlier. What is the outlier cutoff formula?

An outlier is a data point that’s abnormally distant from the rest of the data set. The outlier cutoff formula is “high outliers are greater than 1.5*IQR” and “low outliers are less than 1.5 IQR”

If a distribution is symmetric, what does its histogram look like?

The distribution’s histogram could have a single peak with tails on both sides.

If a distribution is skewed right, what does its histogram look like?

The distribution’s peak will rest on the left side, while its tail will lie on the right side.

If a distribution is skewed left, what does its histogram look like?

The distribution’s peak will be on the right side, while its tail will be on the left side.

How is the stemplot of a distribution related to its histogram?

Both depict frequency

When is it advantageous to split stems on the stemplot?

Split stems depict the shape of a dataset

What is the purpose of a back-to-back stemplot?

Back-to-back stemplots help when comparing the shape, center, and spread of two data sets

In statistics, what are the most common measurements of center?

The most common measurements of center are median and mean.

Explain how to calculate the median, M.

Determine the value in the dead middle, or add the two middle values together and divide by 2

Explain why the median is resistant to extreme observations, but the mean is nonresistant.

The mean is not resistant since outliers can shift the graph. On the other hand, medians are not affected since they focus on middle points as opposed to the values of points and outliers.

In statistics, what is meant by spread?

Spread is how similar or varied the set is for a total dataset.

Explain how to calculate Q1 and Q3.

The formula to calculate Q1 is (n+1) 1/4; the formula to calculate Q3 is (n+1) * 3/4

What is the five-number summary? What can you make from it?

The five-number summary consists of the minimum, 1st quartile, mean, 3rd quartile, and maximum of a dataset. These values are used to form boxplots.

What does IQR stand for and how do you calculate it?

IQR stands for interquartile range, and is calculated by finding the difference of the 3rd quartile and 1st quartile.

What does standard deviation measure?

The average/typical distance from a data point to the mean

What is the relationship between variance and standard deviation?

Variance is standard deviation squared.

When does standard deviation equal zero?

When all the data points are equivalent to the mean

Is standard deviation resistant or nonresistant to extreme observations? Explain.

Standard deviation is nonresistant to extreme observations. Since mean values are nonresistant and connected to standard deviation, standard deviations will likely be connected too.

How do you determine which measures of center and spread to use?

Symmetric graphs need mean while skewed graphs need resistant measures like median and IQR

What are some keywords to use when comparing distributions of quantitative data?

More than, less than, more skewed, slightly, etc etc. Mainly just comparative words

What is a percentile?

A percentile is a value/score that indicates the percentage of values of an equal or lesser value within the data set

What is a cumulative relative frequency graph?

A visual chart depicting the running total of frequencies in a data set.

Explain how to standardize a variable.

To standardize a variable. change its scale to make the mean 0 and the standard deviation 1. This can be done through the z-score formula— ( “x” - mean ) / standard deviation

What is the purpose of standardizing a variable?

Standardizing variables can make them easier to compare with each other.

Explain how additions and multiplications transform data. Explain their effect on measures of center and on measures of spread.

Additions of a constant to a distribution shift the distribution right; this doesn’t affect measures of spread, but it adds to the measures of center. Multiplying a spread does not change its distributions; it multiplies the measures of spread and center.

Is there a difference between the 80th percentile and the top 80%? Explain.

With the 80th percentile, 80% of scores are equal or below yours, while top 80% means that only 20% of scores are below yours.

What does the area under a density curve represent?

The area under a density curve represents the proportion of all observations that fall within that range.

Where is the median of a density curve located?

The median of a density curve is located in the equal-areas point, which splits the area in half.

What is a uniform distribution?

A uniform distribution is a probability distribution where each outcome has an equal chance of occuring.

How would you describe the shape of normal curve?

The shape of a normal curve is symmetric, single-peaked, and mound-shaped.

How do you determine if a distribution of quantitative data is approximately normal using numerical evidence?

Use the empirical rule

What is a standard normal distribution?

A normal distribution with a mean of 0 and a standard deviation of 1.

What information does the standard normal table give?

The table gives the probability, or area under a bell curve, between any two z-scores

Explain the Empirical Rule.

The Empirical Rule states that, in a normal distribution with the mean and standard deviation of a population, 68% of values will fall within 1σ of the mean, 95% of values will fall within 2σ of the mean, and 99.7% of values fall within 3σ of the mean.