Statistic: Ch 12

Standard deviation can only be zero or positive, never negative.

Which one of the following is NOT a correct statement about standard deviation.

True

: The unit of measure for the median is the same as the unit of measure of the data.

Boxplot

A ______________ is a graph of a five-number summary.

Sum of observations/n

A shopper at a local supermarket spent an average of $32.92 in her last eight trips to the store. Which of the following expressions represents the mean of this data set?

False

If a histogram is skewed to the right, then the corresponding boxplot will have a long line on the left or lower end.

True

If a histogram is symmetric, then the corresponding boxplot will also be symmetric.

Stemplot and Histogram

If we have data on a single quantitative variable, which of the following graphs are a best to show the distribution of the data?

False

In a boxplot, a box spans from the minimum to the maximum.

Skewed

Since the mean is much larger than the median, what shape do you predict that the histogram of the CEO's annual salaries to have?

True

The entire boxplot spans from the minimum value of a data set to the maximum value.

Left skewed

The five-number summary of test scores in an introductory statistics class is: Min = 23% Q1 = 71% Median = 83%, Q3 = 86% and Max = 100%. What is the shape of the boxplot for these data?

True

The long "whisker" on the right side of the boxplot indicates that the GNP's between the 3rd quartile and the maximum are very spread out.

True

The longer the boxplot, the more variable the data displayed in the boxplot.

Answer 1: center Answer 2: variability

The simplest useful description of a distribution consists of __________both a measure of and a measure of _________.

Median will not change.

There are eight boys in a pre-school class. Their mean height is 33 inches and their median height is and 33 inches. The tallest boy whose height is 38 inches moves away and is replaced by a boy whose height is 39 inches. How does this affect the median?

True

True or false: A boxplot is a graphical representation of the five-number summary.

False

True or false: Because the length of the box is short compared to the line on the right side of the boxplot, we know that the GNP's are very spread out in this interval.

False

True or false: If the histogram is symmetric, then the distance between each of the five numbers is the same.

True

True or false: The larger the distance between two adjacent numbers in the five-number summary, the more spread out the data in that interval.

True

True or false: The line drawn in the box of a boxplot indicates the location of the median.

standard deviation

Variance is the square of the _____.

Five-number summary and mean and standard deviation

What are the two common descriptions of center and variability?

The value that cuts the ordered data in half

What does the median represent?

(n + 1)/2, where n is the number of observations

What formula is used to find the value of the median?

Mean and median

Which are measures of the location of data on the number line?

range, interquartile range, standard deviation

Which are measures of the spread of data about the center?

Median

Which measure do you think is the better measure of center for the CEO's annual salaries?

Outliers affect the mean because every observation in a data set (including outliers) is used to compute it.

Which measure is affected by outliers?

Strong skewness affects the mean, so the median is a better measure of center for skewed data.

Which measure is best for strongly skewed data?

The mean is preferred over the median because it has nice mathematical properties whenever there are not outliers or strong skewness.

Which measure is best for symmetric data without outliers?

average of the observations

Which of the following describes the mean of a set of numerical observations?

Standard deviation measures variability as a kind of average distance from the mean, so use it only with the mean. Median is the midpoint of a distribution The first quartile is the median of the observations whose position in an ordered list is to the left of the location of the overall median.

Which of the following statements are true?

Because the histogram is strongly right-skewed

Why is the median the preferred measure of center?