Chapter 3 Math

If all the data values in a set are​ identical, what can you conclude about the standard​ deviation?

The standard deviation is zero.

Central Tedency

Center around a particular value to gather in a category rather than spread themselves across the range among the available categories

What is an advantage of using the range as a measure of​ variation?

It is easy to compute.

What is a disadvantage of using the range as a measure of​ variation?

It uses only two entries from the data set

Which is not a measure of​ dispersion?

Mean

Which measure of center must be equal to an actual data​ value? Explain why.

Since the mode is the most frequent observation that occurs in the data​ set, it must be an actual value from the data set.

If a professor adds 10 points to each​ student's final exam​ score, how will it affect the distribution of final exam​ scores?

The center will​ change, but the shape and spread will remain the same

If the standard deviation for a data set is​ zero, what can you conclude about the​ data?

The data values must all be equal.

Which statement is not true regarding the​ mean?

The mean is always the best measure of center.

Which statement is not true regarding the​ median?

The median is always one of the values in the data set.

Which measure of center​ (mean or​ median) is​ resistant? Explain what it means for that measure to be resistant.

The median is resistant because it is not sensitive to extreme values in the data set. If the largest observation was​ doubled, for​ example, the median would not change since that largest value does not factor into its computation.

If the standard deviation of a variable is​ 0, then the mean is equal to the median.

True

The range measures the spread of a distribution. It is the distance from the smallest value to the largest value. Is the range sensitive to the presence of​ outliers?

Yes

Mean

average not a resistant measure

What measure of central tendency best describes the​ "center" of the​ distribution?

median

Median

the middle score in a distribution; half the scores are above it and half are below it a resistant measure

Mode

the most frequently occurring score(s) in a distribution a resistant measure

In distributions that are skewed to the​ right, what is the relationship of the​ mean, median, and​ mode?

mean​ > median​ > mode

The data value that occurs with the greatest frequency is called the

mode

In distributions that are skewed to the​ left, what is the relationship of the​ mean, median, and​ mode?

mode​ > median​ > mean

Variance is the square root of standard deviation.

False

Which distribution shape​ (skewed left, skewed​ right, or​ symmetric) is most likely to result in the mean being substantially smaller than the​ median?

A distribution that is skewed left will likely have a mean that is smaller than the median since the extreme values in the tail tend to pull the mean to the left.

Explain the relationship between variance and standard deviation. Can either of these measures be​ negative? Explain.

The standard deviation is the positive square root of the variance. The standard deviation and variance can never be negative. Squared deviations can never be negative.

Explain why it is misleading to use the term​ "average" to describe your typical bowling score.

The word​ "average" is ambiguous and can refer to any measure of center. It is better to use the specific measure of center you intend​ mean, median, or​ mode.

Name and describe the three most important measures of center.

The​ mean, median, and mode are the most important measures of center. The mean of a data set is its arithmetic average. The median of a data set is the middle value in its ordered list. The mode of a data set is its most frequently occurring value.

When comparing two populations with the same variable of interest in the same unit of​ measure, the larger the standard​ deviation, the (blank) dispersion there is in the distribution.

Mode