Stats Chapter 3 Terms & Questions

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.

Which of the following is NOT a measure of​ center?

Census A census is the collection of data from every member of the population. It is not a measure of center.

The ________ is found by adding all the data values and dividing by the total number of values.

Mean The mean is what is typically considered the average.

When an odd number of data values are arranged in​ order, the​ _________ is the middle value.

Median The median divides the data set in half.

If the maximum and minimum values in a data set are​ averaged, the result is the​ ______?

Midrange This measure of center is useful for centering a graph. to solve: (max data value)+(min data value)/2

The measure of center that is the value that occurs with the greatest frequency is the?

Mode

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

Mode The mode is the value that occurs with the greatest frequency. The mode can be useful for predicting future results based on the different frequencies of past results.

Empirical Rule

a rule helpful for interpreting data values for a standard deviation; rule states that for data having a distribution that is bell shaped, these properties apply: - about 68% of all values fall within 1 standard deviation of the mean - about 95% of all values fall within 2 standard deviations of the mean - about 99.7% of all values fall within 3 standard variations of the mean

The value that divides a histogram into two equal areas is called the ____? The value that serves as a balancing point for a histogram is the _____?

median, mean

The Range Rule of Thumb roughly estimates the standard deviation of a data set as_____?

s=range/4

A data value is considered​ _______ if its​ z-score is less than minus−2 or greater than 2.

sig low or sig high; A data value is considered significantly low or significantly high when it lies far from the mean. We define data values that are farther than 2 standard deviations below the mean as significantly low and values that are farther than 2 standard deviations above the mean as significantly high

For data sets having a distribution that is approximately​ bell-shaped, _______ states that about​ 68% of all data values fall within one standard deviation from the mean.

the Empirical Rule; for data sets having a distribution that is approximately​ bell-shaped, the Empirical Rule states that about​ 68% of all data values fall within one standard deviation from the mean.

What happens whenever a data value is less than the​ mean?

the corresponding z-score is negative; A negative​ z-score indicates a data value is less than the mean.

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

the data values must all be equal; Standard deviation measures spread. If there is no​ spread, one can conclude that the values are all the same.

The square of the standard deviation is called the​______?

variance; meaning and is equal to the square of the standard deviation.

When a data value is converted to a standardized scale representing the number of standard deviations the data value lies from the​ mean, we call the new value a​____?

z-score; The term​ z-score represents a standardized value and is the number of standard deviations that a given​ x-value is above or below the mean.