1. Which of the following is not true about histograms?
A. The bars must touch each other.**
B. A histogram may be symmetric or skewed depending on the selection of bin width
C. Each bin must have the same width.
D. Histograms may represent categorical data.
E. Histograms may have gaps or clusters.
2. Suppose that a frequency histogram and a cumulative frequency histogram are constructed from the same set of data, using the same classes. Then, for each class,
A. the frequency is less than the cumulative frequency
B. the frequency is less than or equal to the cumulative frequency**
C. the frequency is equal to the cumulative frequency
D. the frequency is greater than or equal to the cumulative frequency
3. When ordering doors for new construction, the following variables are specified. Which of these variables is quantitative?
A. Purpose of door: interior or exterior.
B. Width of door: opening in inches.**
C. Core of door: solid core or hollow core.
D. Color of door: White, oak stain, natural, or ivory.
4. Which of the following statements are true?
1) Stemplots are useful for both quantitative and categorical data.
2) Stemplots are equally useful for both small and large data sets.
3) Stemplots can show symmetry, gaps, clusters, and outliers in the data.
A. 1 only
B. 2 only
C. 3 only
D. 1 and 3
E. 2 and 3**
1. To determine which of the statements about histograms is not true, we can carefully analyze each option:
A. The bars must touch each other. - This is true for histograms. The bars represent the different intervals or bins, and they should be adjacent to each other.
B. A histogram may be symmetric or skewed depending on the selection of bin width - This is true. The shape of a histogram can vary depending on the chosen width of the bins. It can be symmetric or skewed.
C. Each bin must have the same width. - This is true for histograms. To maintain consistency, each bin should have the same width.
D. Histograms may represent categorical data. - This is true. While histograms are commonly used to represent quantitative data, they can also be used for categorical data. In this case, the bars would represent different categories and their frequencies.
E. Histograms may have gaps or clusters. - This is false. In a histogram, the bars should be contiguous (touching each other) and not have gaps or clusters.
Therefore, the correct answer is A. The bars must touch each other. This statement is not true about histograms.
2. The question asks about the relationship between a frequency histogram and a cumulative frequency histogram for each class. Let's examine the options:
A. the frequency is less than the cumulative frequency - This is not necessarily true. In a frequency histogram, each bar represents the frequency of values falling within a specific class. In a cumulative frequency histogram, each bar represents the cumulative frequency up to that class. The frequency can be equal to or less than the cumulative frequency.
B. the frequency is less than or equal to the cumulative frequency - This is the correct answer. In a cumulative frequency histogram, each bar represents the cumulative frequency up to that class. Since the frequency includes all the values up to that class, it will be less than or equal to the cumulative frequency.
C. the frequency is equal to the cumulative frequency - This is incorrect. As explained in option A, the frequency can be less than or equal to the cumulative frequency, but it is not always equal to it.
D. the frequency is greater than or equal to the cumulative frequency - This is incorrect. The frequency represents the number of occurrences within a specific class, while the cumulative frequency is the sum of frequencies up to that class. Therefore, the frequency cannot be greater than or equal to the cumulative frequency.
Therefore, the correct answer is B. The frequency is less than or equal to the cumulative frequency for each class.
3. The question asks which of the specified variables is quantitative. Let's analyze each variable:
A. Purpose of door: interior or exterior - This is a categorical variable, as it represents different categories or labels.
B. Width of door: opening in inches - This is the correct answer. Width of door is a quantitative variable because it represents a numerical measurement.
C. Core of door: solid core or hollow core - This is a categorical variable, as it represents different categories or labels.
D. Color of door: White, oak stain, natural, or ivory - This is a categorical variable, as it represents different categories or labels.
Therefore, the correct answer is B. Width of door: opening in inches is the quantitative variable.
4. The question asks us to determine which statements are true about stemplots. Let's examine each statement:
1) Stemplots are useful for both quantitative and categorical data - This is false. Stemplots, also known as stem-and-leaf plots, are specifically designed to effectively represent quantitative data. Categorical data is better visualized using other graphical representations such as bar charts or pie charts.
2) Stemplots are equally useful for both small and large data sets - This is false. Stemplots tend to become less useful for large data sets due to their potential for becoming cluttered and difficult to interpret. While stemplots can be useful for small data sets, other graphical representations like histograms or boxplots may be more appropriate for larger data sets.
3) Stemplots can show symmetry, gaps, clusters, and outliers in the data - This is true. Stemplots can help identify patterns of symmetry in the distribution of quantitative data. Additionally, they can reveal gaps, clusters, and outliers by visualizing the spread of values from the stem and leaves.
Therefore, the correct answer is E. 2 and 3. Statements 2 and 3 are true about stemplots.