3.1 Assignment
What is the symbol used to represent the sample mean?
-x
If you have only a frequency distribution and not the original data, how do you approximate the mean?
Assume that every value in a class is equal to the midpoint of that class.
Which statement is NOT true regarding modes?
Every data set has at least one mode.
An association of Realtors reports state-by-state median existing-home prices for each quarter. Why do you suppose they use the median instead of the mean? What might be the disadvantage of reporting the mean?
Home prices are probably skewed to the right and not symmetric. This makes the median a better representation of the center than the mean which would be influenced by the extremely high priced homes. Reporting the mean would give the impression that the "typical" home price is higher than it is.
Which of the following is always true?
In a symmetric and bell-shaped distribution, the mean, median, and mode are the same.
Suppose the list below shows how many text messages Elyse sent each day for the last 10 days. If Elyse wants to know how many text messages she typically sends each day, which measure of central tendency better describes the typical number of text messages per day?
Median; The median of 27.5 is a better representative of the center since it is resistant to the one extreme value. The mean of 33.3 is not representative of the typical number of texts since only one number is larger than the mean.
A magazine published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S. drivers? Why or why not?
No, the value of 27.3 cents is not the mean because the 50 amounts are all weighted equally in the calculation, but some states consume more gas than others, so the mean amount of state sales tax should be calculated using a weighted 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.
A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. What is the relationship between the mean and the median for this data?
The mean and median will be roughly equal since the distribution is fairly symmetric.
Which statement is NOT true regarding the mean?
The mean is always the best measure of center.
Which of the following is NOT a characteristic of the mean?
The mean is called the average by statisticians.
A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. What is the relationship between the mean and the median for this data?
The mean will be substantially larger than the median since the distribution is skewed right.
A sample of thirty users of a popular social networking site yielded the histogram on the right for the number of friends. Which measure of central tendency better describes the "center" of the distribution?
The median is a better of measure of the center of the data since the distribution is skewed to the right.
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.
Without performing any calculations, determine which measure of central tendency best represents the graphed data. Explain your reasoning.
The median is the best measure because the data are skewed.
A defunct website listed the "average" annual income for Florida as $35,031. What is the role of the term average in statistics? Should another term be used in place of average?
The term average is not used in statistics. The term mean should be used for the result obtained by adding all of the sample values and dividing by the total number of sample values.
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).
Which of the following is NOT a measure of center?
census
Methods used that summarize or describe characteristics of data are called _______ statistics.
descriptive
The ___________ is found by adding all the data values and dividing by the total number of values.
mean
A value at the center or middle of a data set is a(n) _______.
measure of center
When an odd number of data values are arranged in order, the _________ is the middle value.
median
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
If the maximum and minimum values in a data set are averaged, the result is the __________.
midrange
The measure of center that is the value that occurs with the greatest frequency is the _______.
mode
The only measure of center that can be found for both quantitative and qualitative data is the ______________.
mode
