Question 1

A descriptive measure that is NOT measured in the same units as the original data is the variance.

Accepted Answer

Variance is measured in the units of the original data squared, not in the original units themselves.

Question 2

Since the population size is always larger than the sample size, a sample statistic can never be larger than the population parameter.

Accepted Answer

Sample statistics can sometimes be larger than population parameters due to sampling variability. For example, if you are measuring income, a sample might by chance include more high-income individuals than the population average, leading to a sample mean higher than the population mean.

Question 3

If a distribution has a shape that is positively skewed, this means that it has an elongated tail that extends in the right-hand direction.

Accepted Answer

In a positively skewed distribution, the tail is longer on the right side, indicating that there are a number of values greater than the mode that extend towards higher values.

Question 4

The descriptive measures (mean, variance, and standard deviation) will yield different values for a relative frequency distribution versus a frequency distribution, for the same data set.

Accepted Answer

The descriptive measures such as mean, variance, and standard deviation will yield the same values for a relative frequency distribution and a frequency distribution for the same data set because relative frequency is just the frequency of each category divided by the total number of observations, which does not affect these overall summary statistics.

Question 5

In a cumulative frequency distribution, we can show directly the number of data set members at or below any specified value.

Accepted Answer

In a cumulative frequency distribution, the count at each point includes all data up to and including that point, showing the total number of observations at or below any specified value.

Question 6

In a bar chart, the height of the vertical bar represents the x value.

Accepted Answer

In a bar chart, the height of the vertical bar represents the value of the data point, which is typically plotted on the y-axis, not the x-axis. The x-axis usually represents the categories being compared.

Question 7

On the horizontal axis of a bar chart, one places the frequency or the relative frequency (but only one).

Accepted Answer

In a bar chart, the horizontal axis typically represents the categories being compared, while the vertical axis represents the frequency or relative frequency.

Question 8

The range is the difference between the smallest and largest values in the data set.

Accepted Answer

The range is calculated by subtracting the smallest value in the data set from the largest value.

Question 9

The median identifies the data set center by establishing a value such that at least half the numbers in the data set are at or above that value and at least half the numbers are at or below.

Accepted Answer

The median is indeed the middle value in a data set, ensuring that half the numbers are above it and half are below it, effectively identifying the center of the data set.

Question 10

The relative frequency of a class is the proportion of the number of members in that class.

Accepted Answer

The relative frequency of a class is calculated by dividing the number of members in that class by the total number of members in all classes, thus representing the proportion of members in that specific class.

Question 11

The most frequently occurring value of a data set is called the mode.

Accepted Answer

The mode is defined as the value that appears most frequently in a data set.

Question 12

The sample variance has the value n in the denominator while the population variance has the value n-1 in the denominator.

Accepted Answer

The sample variance typically has $n-1$ in the denominator to correct for bias in estimating the population variance, while the population variance uses $n$ in the denominator.

Question 13

If there are an odd number of items in a data set, the median is the average of the values of the two middle items.

Accepted Answer

When there is an odd number of items in a data set, the median is the value of the middle item, not the average of two items.

Question 14

In general, when a data set shows positive skewness, the mean will be smaller than the median; for negatively skewed data, the mean will be larger than the median.

Accepted Answer

In a positively skewed distribution, the mean is typically larger than the median due to the long tail on the right pulling the mean upwards. Conversely, in a negatively skewed distribution, the mean is usually smaller than the median because the long tail on the left drags the mean down.

Question 15

The mean serves to act as a balancing point for the data.

Accepted Answer

The mean (average) of a data set is the point at which the total amount of deviations above and below it sum to zero, effectively balancing the dataset.

Question 16

The standard deviation is approximately the average distance between the individual values in the data set and the data set center (i.e., the mean).

Accepted Answer

The standard deviation measures the amount of variation or dispersion in a set of values, and it is indeed a way to quantify the average distance between each data point and the mean of the dataset.

Question 17

When calculating the median of an ordered data set with an odd number of items, the median is the value of the middle item.

Accepted Answer

In an ordered data set with an odd number of items, the median is indeed the value of the middle item, as it divides the data set into two equal halves.

Question 18

The most frequently occurring value of a data set is called the mean.

Accepted Answer

The most frequently occurring value of a data set is called the mode, not the mean. The mean is the average of all the values in a data set.

Question 19

In a frequency distribution, x represents the possible values and f(x) represents the counts or frequencies of those values.

Accepted Answer

In a frequency distribution, "x" typically represents the different values or categories being observed, and "f(x)" represents the frequency or count of each of those values, indicating how often each value occurs.

Question 20

The mean absolute deviation (MAD) measures the average absolute distance of data points from the mean of the data set.

Accepted Answer

The mean absolute deviation (MAD) is a measure of variability that indicates the average distance between each data point and the mean of the data set, taking the absolute value of each distance to ensure it is non-negative.

Quiz 2: Descriptive Statistics I: Elementary Data Presentation and Description