chapter 3 homework

Which of the following is always​ true? A. Data skewed to the right have a longer left tail than right tail. B. In a symmetric and​ bell-shaped distribution, the​ mean, median, and mode are the same. C. For skewed​ data, the mode is farther out in the longer tail than the median. D. The mean and median should be used to identify the shape of the distribution.

B. In a symmetric and​ bell-shaped distribution, the​ mean, median, and mode are the same. - Explanation: A distribution of data is symmetric if the left half of its histogram is roughly a mirror image of its right half. In this​ case, the​ mean, median, and mode are the same.

Which of the following is NOT a characteristic of the​ mean? A. The mean is sensitive to outliers. B. The mean is called the average by statisticians. C. The mean takes every data value into account. D. The mean is relatively reliable.

B. The mean is called the average by statisticians - Explanation: The term average is not used by statisticians and is considered ambiguous.

Which of the following is NOT a measure of​ center? Mode, Mean, Cencus, Median

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

Which of the following is NOT a value in the​ 5-number summary?

Mean -Explanation: The mean is not included in the​ 5-number summary.

Fill in the blank. A value at the center or middle of a data set is​ a(n) _______.

Measure of Center - Explanation: A measure of center is a value at the center or middle of a data set. There are several different ways to determine the​ center, so there are different definitions of measures of​ center, including the​ mean, median,​ mode, and midrange.

Fill in the blank. The measure of center that is the value that occurs with the greatest frequency is the​ _______.

Mode -Explanation: The mode is the most frequently occurring data value and is the appropriate measure of center for nominal data. Next Question

Fill in the blank. In modified​ boxplots, a data value is​ a(n) _______ if it is above Q3+​(1.5)(IQR) or below Q1−​(1.5)(IQR).

Outlier - Explanation: For the purposes of constructing modified​ boxplots, outliers are any data values above Q3+​(1.5)(IQR) or below Q1−​(1.5)(IQR).

Which measure of variation is most sensitive to extreme​ values?

Range -Explanation: Extreme values will affect the value of the range.

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

Refer to the boxplots available below that are drawn on the same scale. One boxplot represents weights of​ men, and the other boxplot represents weights of women. Which boxplot represents weights of​ women? Explain.

The bottom boxplot represents weights of women because it depicts weights that are generally lower.

calc median

The median of a data set is the middle value when the data values are arranged in order of magnitude. If the number of data values is​ even, the median is found by computing the mean of the two middle numbers in the sorted list. median= (greater 'middle' value + lesser 'middle' value)/2

If your score on your next statistics test is converted to a z​ score, which of these z scores would you​ prefer: −​2.00, −​1.00, 0, 1.00,​ 2.00? Why?

The z score of 2.00 is most preferable because it is 2.00 standard deviations above the mean and would correspond to the highest of the five different possible test scores. -Explanation: A z score​ (or standardized​ value) is the number of standard deviations that a given value x is above or below the mean. A negative z score corresponds to an x value less than the mean. A positive z score corresponds to an x value greater than the mean. The more negative the z​ score, the further the x value is below the mean. The more positive the z​ score, the further the x value is above the mean.

Geometric mean Calculation

Used for average growth calculation/rate

Fill in the blank. The square of the standard deviation is called the​ _______.

Variance -Explanation: The term variance has a specific statistical meaning and is equal to the square of the standard deviation.

Which of the following is NOT a property of the standard​ deviation? A. The standard deviation is a measure of variation of all data values from the mean. B. When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations. C. The units of the standard deviation are the same as the units of the original data. D. The value of the standard deviation is never negative.

When comparing variation in samples with very different​ means, it is good practice to compare the two sample standard deviations. -Explanation: It is not a good practice to compare the two sample standard deviations in samples with very different means.

Fill in the blank. 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 -Explanation: 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.

Identify the symbols used for each of the​ following: a. The symbol for sample standard deviation is b. The symbol for population standard deviation is c. The symbol for sample variance is d. The symbol for population variance is

a. The symbol for sample standard deviation is s b. The symbol for population standard deviation is σ c. The symbol for sample variance is s^2 d. The symbol for population variance is σ^2

Fill in the blank. Methods used that summarize or describe characteristics of data are called​ _______ statistics.

descriptive statistics - Explanation: Descriptive statistics are methods and tools that summarize or describe relevant characteristics of data.

The Range Rule of Thumb roughly estimates the standard deviation of a data set as​ _______.

s=Range/4

Fill in the blank. A data value is considered​ _______ if its​ z-score is less than −2 or greater than 2.

significantly low or significantly high -Explanation: 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.

Fill in the blank. Whenever a data value is less than the​ mean, _______.

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

A random sample of 10 subjects have weights with a standard deviation of 10.335110.3351 kg. What is the variance of their​ weights? Be sure to include the appropriate units with the result. we know SD = variance ^2

therefore, Variance= 106.8143 kg^2