Question 1

A box plot shows the skewness of a distribution.

Accepted Answer

A box plot can show the skewness of a distribution by presenting the distribution’s median, quartiles, and outliers. If the median is closer to the lower quartile, the distribution is negatively skewed, and if it is closer to the upper quartile, it is positively skewed. The length and position of the whiskers and the presence of outliers can also indicate the skewness of the distribution.

Question 2

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

Accepted Answer

The box in a box plot extends from the 25th percentile (Q1) to the 75th percentile (Q3), which represents the interquartile range.

Question 3

A scatter diagram of sales versus production may be constructed by plotting the minimum, first quartile, median, third quartile, and the maximum values of each variable.

Accepted Answer

A scatter diagram is a graph that shows the relationship between two variables, typically with one variable on the x-axis and the other variable on the y-axis. To construct a scatter diagram, data points should be plotted for each pair of values, not just summary statistics such as the minimum, quartiles, and maximum values.

Question 4

Quartiles divide a distribution into four equal parts.

Accepted Answer

Quartiles divide a distribution into four equal parts: Q1, Q2 (median), Q3.

Question 5

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

Accepted Answer

A negatively skewed distribution means that the majority of the data is on the right side of the distribution and the long tail extends to the left, indicating that there are some extreme low values in the data. This makes the distribution asymmetrical.

Question 6

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

Accepted Answer

The coefficient of skewness is calculated by dividing the difference between the mean and mode by the standard deviation.

Question 7

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 8

Percentiles divide a distribution into 100 equal parts.

Accepted Answer

Percentiles divide a distribution into 100 equal parts, with each percentile representing the percentage of the data that falls below a certain value. For example, the 75th percentile is the value at which 75% of the data falls below and 25% falls above.

Question 9

A dot plot is useful for showing individual observations.

Accepted Answer

A dot plot is a simple chart that displays individual observations along a number line or horizontal axis. It is often used to show the distribution of a set of data and is particularly useful for small data sets.

Question 10

A scatter diagram is used to illustrate a relationship between gender and the preference for Coke or Pepsi.

Accepted Answer

A scatter diagram is typically used to illustrate the relationship between two quantitative variables, not categorical variables like gender and preference for Coke or Pepsi. For categorical variables, a bar chart or pie chart would be more appropriate.

Question 11

A dot plot shows the symmetry of a distribution.

Accepted Answer

A dot plot can show the symmetry of a distribution by visually representing data points and their frequency, allowing one to see if the data is symmetrically distributed around a central value.

Question 12

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

Accepted Answer

The 50th percentile is the median, which may or may not be equal to the mean, depending on the shape of the distribution. The rest of the statement is nonsensical and does not make logical sense.

Question 13

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 students, since they scored in the 85th percentile.

Question 14

Quartiles divide a distribution into 10 equal parts.

Accepted Answer

Quartiles divide a distribution into 4 equal parts, not 10.

Question 15

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

Accepted Answer

A dot plot displays individual data points as dots, providing a clear representation of the spread and distribution of the data, making it useful for showing the range of the data.

Question 16

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

Accepted Answer

This is true because scatter diagrams typically plot one variable on the Y-axis and another variable on the X-axis, with the goal of seeing if there is a relationship or correlation between the two variables. In this case, sales and production are being compared to see if there is a correlation between the two.

Question 17

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 18

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

Accepted Answer

A box plot typically shows the minimum, maximum, 25th percentile, 50th percentile (median), and 75th percentile of a dataset. It does not typically show the percentiles listed in the question.

Question 19

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 visualize small data sets and the frequency of each value in the data set. It involves placing dots above the corresponding value on a number line, with the height of the dot representing the frequency of that value.

Question 20

A relationship between two nominal variables is summarized by a contingency table.

Accepted Answer

A contingency table is used to display the relationship between two nominal variables.

Quiz 4: Describing Data: Displaying and Exploring Data