Question 1

If the distribution is asymmetric, which measure of location is most appropriate if the data is in a nominal scale? If it is in an ordinal scale? If it is in an interval or ratio scale?

Accepted Answer

The answer of If the distribution is asymmetric, which measure...

Question 2

A mathematical distribution whose objective is to obtain a count of the number of responses associated with different values of one variable and to express these counts in percentage terms is called ________.

Accepted Answer

A frequency distribution is a distribution of observed responses that counts the occurrences of different values of one variable and expresses these counts in percentage terms. Sampling distribution refers to the distribution of a statistic based on random samples from a population. Random distribution is not a commonly used term in statistics. Systematic distribution refers to a pattern in which data is distributed based on a systematic process or rule. Chi-square distribution refers to a distribution that arises in hypothesis testing and is used to test the goodness of fit or independence of categorical data.

Question 3

The ________ is a good measure of location when the variable is inherently categorical or has otherwise been grouped into categories.

Accepted Answer

The mode is the best measure of location for categorical data as it represents the most frequently occurring category or value. The mean and median are more appropriate for continuous numerical data, while maxima refer to the highest value in a set, which may not always be representative of the data as a whole. Categorical listing may be useful for displaying the data, but it is not a measure of location.

Question 4

A frequency distribution ________.

Accepted Answer

A frequency distribution contains information about the distribution of a variable, including the presence of outliers and the shape of the distribution, and it can also be used to create the margins of a contingency table. Therefore, all of the options are correct.

Question 5

Data collected in social media often lend themselves to basic analysis involving frequencies, percentages and cross-tabulations.

Accepted Answer

Data collected in social media can easily be analyzed using basic statistical methods such as frequencies, percentages and cross-tabulations.

Question 6

A measure of central tendency given as the value that occurs the most in a sample distribution is called the ________.

Accepted Answer

The mode is the value that occurs the most in a sample distribution. The mean (A) is the average of all the values in the sample, the median (B) is the middle value when the sample is put in order, and the maxima (D) is the highest value in the sample. Trend (E) does not necessarily refer to a measure of central tendency.

Question 7

A measure of central tendency given as the value above which half of the values fall and below which half of the values fall is called the ________.

Accepted Answer

This definition describes the median, which is the middle value when the data are arranged in order. Half of the values fall below the median and half fall above it. The mean is the average of all the values, the mode is the value that appears most frequently, and the maxima refers to the highest values in the data set. Binary inflection is not a statistical term.

Question 8

If the distribution is asymmetric and the variable is measured on a nominal scale, the ________ should be used as a measure of location.

Accepted Answer

The mode is the most appropriate measure of location for data that is asymmetric and measured on a nominal scale, as it represents the most frequently occurring category or value within the dataset. Mean and median are not suitable for nominal data, and maxima and trend do not apply to measures of central tendency.

Question 9

According to the text, which of the following represents the highest peak of the distribution?

Accepted Answer

The mode represents the highest peak of a distribution, as it is the value that appears most frequently in the data set.

Question 10

Which of the following is NOT a statistic that is associated with the measures of location of frequency distribution?

Accepted Answer

Maxima is not a measure of location but rather a measure of spread or variability. The mean, mode, and median are all measures of location that describe the central tendency of a distribution.

Question 11

The most common measures of variability are the ________ and ________.

Accepted Answer

The range and variance are the most common measures of variability. The range is a simple measure of the spread of data, calculated as the difference between the highest and lowest values in a dataset. The variance is a more sophisticated measure that takes into account how much each individual value differs from the mean of the dataset. Together, these measures can provide a good indication of how spread out or tightly clustered a set of data is.

Question 12

A frequency distribution for a variable produces ________.

Accepted Answer

A frequency distribution produces a table of frequency counts, percentage, and cumulative percentages for a given variable. Therefore, all of the options given in the question (A, B, C) are correct.

Question 13

Which of the following is used to estimate the average when the data have been collected using an interval or ratio scale?

Accepted Answer

The mean is used to estimate the average when data have been collected using an interval or ratio scale, as it involves arithmetic calculations that are meaningful for these levels of measurement.

Question 14

The chi-square statistic can be estimated on counts of data or on percentages.

Accepted Answer

The answer of The chi-square statistic can be estimated on...

Question 15

The ________ should be used as a measure of location if the distribution is asymmetric and the variable is measured on an ordinal scale.

Accepted Answer

The median is the best choice because it is not affected by extreme values or the shape of the distribution, making it a good measure of location for asymmetric distributions. It is also appropriate for variables measured on an ordinal scale, as it only requires the values to be ranked in order. The mean and mode may not be appropriate for asymmetric distributions, and maxima and ranking order are not commonly used measures of location.

Question 16

The ________ is that value obtained by summing the values of all elements in a set and dividing by the number of elements.

Accepted Answer

The mean is the average value of a set and is calculated by summing all the values in the set and dividing by the number of elements in the set. This is the most common measure of central tendency and is often referred to simply as the "average".

Question 17

The ________ of a sample is the middle value when the data are arranged in ascending or descending rank order.

Accepted Answer

The definition provided in the question matches the definition of median.

Question 18

When using the chi-square statistic in cross-tabulation, the null hypothesis (H0)will be rejected only when the probability of obtaining a more extreme value is less than 0.05.

Accepted Answer

This statement is true. A significance level of 0.05 (or 5%) is commonly used as a threshold for rejecting the null hypothesis in statistical tests, including the chi-square test used in cross-tabulation. If the p-value (probability of obtaining a more extreme value) is less than 0.05, it is considered statistically significant and the null hypothesis is rejected. However, if the p-value is greater than or equal to 0.05, the null hypothesis cannot be rejected (i.e., there is insufficient evidence to conclude that there is a significant relationship between the variables being analyzed).

Question 19

According to the text, the ________ is a statistic that describes a location within a data set.

Accepted Answer

The text states that measures of location describe a location within a data set.

Question 20

A statistic that indicates the distribution's dispersion is called ________.

Accepted Answer

Measures of variability, such as standard deviation and range, indicate how spread out the data is and therefore provide information on the distribution's dispersion. Measures of location (e.g. mean, median) provide information on where the data is centered, while measures of association (e.g. correlation coefficient) indicate the strength and direction of the relationship between two variables. Measures of relativity and difference are not commonly used statistical terms.

Quiz 11: Data Analysis: Frequency Distribution, Hypothesis Testing, and Cross-Tabulation