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

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

Answer: s, like the mean, is not resistant. Strong skewness or a few outliers can make s very large.

When does standard deviation equal zero?

When does standard deviation equal zero?

Answer: When there is no spread. This happens only when all observations have the same value.

What is the relationship between variance and standard deviation?

What is the relationship between variance and standard deviation?

Answer: Standard deviation s is the square root of the variance s-squared.

What does standard deviation measure? How do we calculate it?

What does standard deviation measure? How do we calculate it?

Answer: It measures spread around the mean and should only be used when the mean is chosen as the measure of center.

How do we use the five-number summary to make a modified boxplot?

How do we use the five-number summary to make a modified boxplot?

Answer: A modified boxplot is a graph of the 5-number summary, with outliers plotted individually.


- a central box spans the quartiles
- a line in the box marks the median
- observations more than 1.5*IQR outside the central box are plotted individually
- lines extend from the box out to the smallest and largest observations that are not outliers

What is the five-number summary?

What is the five-number summary?

Answer: The 5 # summary is Minimum, Q1, Median, Q3, Maximum.

How can we use IQR to determine outliers?

How can we use IQR to determine outliers?

Answer: An observations is an outlier it if is more than 1.5*IQR above the third quartile of below the first quartile.

What is the interquartile range?

What is the interquartile range?

Answer: The distance between the first and third quartiles, Q3 - Q1.

Explain how to calculate Q1 and Q3.

Explain how to calculate Q1 and Q3.

Answer:

1) arrange the observations in increasing order and locate the median M in the list.
2) Q1 is the median of the observations whose position in the ordered list is to the left of the location of the overall median.
3) Q3 is the median of the observations whose position in the ordered list is to the right of the location of the overall median.

In statistics, what is meant by spread?

In statistics, what is meant by spread?

Answer: Spread is a way to measure the variability of the observations around the center. One of the most common ways to measure spread is to calculate the range of the data. The range is obviously sensitive to extreme measures.

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

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

Answer: The median is resistant because it is only based on the middle one or two observations of the ordered list. The mean is sensitive to the influence of a few extreme observations. Even if there are no outliers a skewed distribution will pull the mean toward the long tail.

Explain how to calculate the median, M.

Explain how to calculate the median, M.

Median M is the midpoint of a distribution, the number such that half the observations are smaller and the other half are larger. To find the median:

1) arrange all the observations in order of size, from smallest to largest
2) if the number of observations is odd, the median M is the center observation of the order list.
3) if the number of observations is even, the median M is the mean of the 2 center observations in the ordered list.

Explain how to calculate the mean, x.

Explain how to calculate the mean, x.

Answer: To find the mean of a set of observations, add their values and divide by the number of observations.

In statistics, what is the most common measurement of center?

In statistics, what is the most common measurement of center?

Answer: arithmetic average, or mean

When is it useful to construct a time plot?

When is it useful to construct a time plot?

Answer: For variables that are measured over time, such as the height of a growing child, seasonal variation, price of a stock.

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

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

Answer: To compare the shapes of 2 distributions.

When is it advantageous to split stems on a stemplot?

When is it advantageous to split stems on a stemplot?

Answer: When each stem has many leaves.

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

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

Answer: A histogram is a shaded in stemplot - on the histogram we lose the individual data values but we keep the overall shape of the distribution.

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

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

Answer: Symmetric = right and left sides are approximately mirror images of each other ; skewed right = right side (larger values) extends much farther out than the left side.

Define outlier.

Define outlier.

Answer: an individual observation that falls outside the overall pattern of the graph.