Question 1

The 50^th percentile of a distribution is the same as the distribution mean.

Accepted Answer

If the 50^th percentile of a distribution is the same as the distribution mean, it would mean that 50% of the data falls below the mean and 50% of the data falls above the mean. However, this is not always the case and depends on the shape of the distribution. In a normal distribution, the mean and median (50th percentile) are the same, but in skewed distributions, they can differ.

Question 2

A dot plot is useful for showing possible outliers.

Accepted Answer

A dot plot displays individual data points as dots, making it easy to spot any potential outliers among the data. Therefore, it is a useful tool for identifying possible outliers in a dataset.

Question 3

A scatter diagram of sales versus production is labeled with sales on the Y-axis and production on the X-axis.

Accepted Answer

A scatter diagram typically has the dependent variable (sales in this case) on the Y-axis and the independent variable (production in this case) on the X-axis.

Question 4

Pearson's coefficient of skewness is a measure of a distribution's symmetry.

Accepted Answer

Pearson's coefficient of skewness measures the asymmetry of a distribution, indicating whether the distribution is symmetrical or skewed to the left or right.

Question 5

If a distribution is negatively skewed, the distribution is not symmetrical and the long tail is to the left.

Accepted Answer

Negatively skewed distributions have a long tail to the left and are not symmetrical.

Question 6

A dot plot is useful for showing the range of the data.

Accepted Answer

A dot plot is a type of graph that uses dots to represent data values. It is particularly useful for showing the range of the data and identifying any outliers or unusual values. Each dot represents one data point, allowing the viewer to easily see the relative frequency and distribution of the data.

Question 7

A box plot shows the relative symmetry of a distribution.

Accepted Answer

A box plot provides information about the distribution's central tendency, spread, and outliers, but it does not indicate the actual symmetry of the distribution.

Question 8

Quartiles divide a distribution into ten equal parts.

Accepted Answer

Quartiles divide a distribution into four equal parts, not ten.

Question 9

A student scored in the 85^th percentile on a standardized test. This means that the student scored lower than 85% of all students who took the test.

Accepted Answer

The student scored higher than 85% of all students who took the test, since they scored in the 85th percentile.

Question 10

A stem-and-leaf diagram shows the actual data values.

Accepted Answer

A stem-and-leaf diagram displays the actual data values instead of grouping them into ranges or categories.

Question 11

The "box" in a box plot shows the interquartile range.

Accepted Answer

The box in a box plot represents the interquartile range, which includes the middle 50% of the data. It extends from the first quartile (Q1) to the third quartile (Q3) and contains the median. The whiskers extend to the minimum and maximum values within 1.5 times the interquartile range, and any points beyond the whiskers are considered outliers.

Question 12

A dot plot is useful for quickly graphing frequencies in a small data set.

Accepted Answer

A dot plot is a simple and effective way to display the frequency of data in a small data set. It involves placing a dot or symbol above a number on a number line for each occurrence of that number in the data set. This allows for easy visualization of the distribution and frequency of the data.

Question 13

A box plot graphically shows the 10^th and 90^th percentiles.

Accepted Answer

A box plot graphically shows the minimum, maximum, median, first quartile (25th percentile), and third quartile (75th percentile). It does not show the specific percentiles mentioned in the statement.

Question 14

A dot plot shows the relative symmetry of a distribution.

Accepted Answer

A dot plot can show the shape of a distribution, which includes its symmetry. A symmetrical distribution will have dots evenly distributed on either side of the center line, while an asymmetrical distribution will have more dots on one side than the other.

Question 15

Percentiles divide a distribution into one hundred equal parts.

Accepted Answer

Percentiles divide a distribution into one hundred equal parts, hence the name "percent" which means "per hundred."

Question 16

In a stem-and-leaf display, the leaf represents a class of a frequency distribution.

Accepted Answer

In a stem-and-leaf display, the leaf represents the individual units or smaller values of the data set, not a class of a frequency distribution.

Question 17

In a stem-and-leaf display, the leaf represents the members of a class in a frequency distribution.

Accepted Answer

In a stem-and-leaf display, the stem represents the classes and the leaf represents the members of each class.

Question 18

A dot plot is an easy way to represent the relationship between two variables.

Accepted Answer

A dot plot is used to display the frequency of individual values in a dataset, not the relationship between two variables. Scatter plots are typically used to represent the relationship between two variables.

Question 19

The coefficient of skewness is the standard deviation divided by the mean.

Accepted Answer

The coefficient of skewness is actually (3 * (mean - median)) / standard deviation.

Question 20

Quartiles divide a distribution into four equal parts.

Accepted Answer

Quartiles divide a distribution into four equal parts, each containing 25% of the data.

Quiz 4: Describing Data: Displaying and Exploring Data

The 50th percentile of a distribution is the same as the distribution mean.