A retail manager collected the following sales-receipt totals from the store's cashiers:
$25, $22, $48, $42, $32, $28, $24, $54, $34, $41, $48
What is the median of this sales-receipt data?
Answer : B
The median is the middle value of a dataset when the data is arranged in ascending order. It is a key descriptive statistic used in data-driven decision making because it is resistant to extreme values.
First, sort the data in ascending order:
22, 24, 25, 28, 32, 34, 41, 42, 48, 48, 54
There are 11 values in total, so the median is the 6th value. The 6th value is $34, making it the median.
The median provides insight into the typical transaction size without being influenced by unusually large receipts. Therefore, the correct answer is B.
A nonprofit organization is asking for donations. It hopes to design an email campaign that will ensure it receives at least $50,000. The campaign will reach 10,000 donors and receive donations with a mean of $10 and a standard deviation of $5.
Which measure should be used to determine the probability of the campaign receiving $50,000?
Answer : D
To determine the probability of achieving a specific monetary threshold, data-driven decision making relies on standardization using the z-score. A z-score measures how many standard deviations a value is from the mean and allows analysts to calculate probabilities using the normal distribution.
In this scenario, the nonprofit wants to assess the likelihood that total donations will reach at least $50,000 given a known mean and standard deviation. The z-score enables conversion of the donation target into a standardized value, which can then be evaluated using probability tables or statistical software.
R-squared measures model fit in regression, the t-statistic is used in hypothesis testing, and the median does not support probability calculations. Therefore, the appropriate measure for determining probability in this context is the z-score, making option D correct.
A researcher seeks to pass a bond issue and asks a sample of respondents who have a bachelor's degree if they are voting in favor of the bond because it would be beneficial to the county.
Which type of error does this represent?
Answer : D
This scenario represents **selection bias**, which occurs when a sample is not representative of the population being studied. In data-driven decision making, valid conclusions depend on collecting data from a sample that accurately reflects the broader population.
By surveying only respondents with a bachelor's degree, the researcher systematically excludes other segments of the population who may have different opinions about the bond issue. Educational attainment may influence voting behavior, making the sample biased toward a particular viewpoint. As a result, the findings cannot be generalized to the entire voting population.
While the wording of the question may be persuasive, the primary statistical error is the **non-random and restricted selection of respondents**. Response bias relates to how participants answer questions, whereas this issue arises before responses are even collected. Faulty operationalization and confusion of causality are not applicable here.
Data-driven decision making stresses ethical sampling practices to avoid misleading conclusions. Therefore, the correct answer is **D**, selection bias.
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For which situation could a scatter diagram be used?
Answer : B
A scatter diagram is used to visually examine the relationship between two quantitative variables. In data-driven decision making, scatter diagrams help analysts assess whether variables move together, whether the relationship is positive, negative, or nonexistent, and whether the relationship appears linear or nonlinear.
Each point on a scatter diagram represents a paired observation of two variables, such as advertising spend and sales revenue or hours studied and test scores. Patterns in the plotted points can suggest correlation, which may later be explored using regression analysis. Scatter diagrams are exploratory tools and do not, by themselves, establish causation.
A prioritization matrix ranks options, frequency differences are examined using bar or Pareto charts, and differences in means are evaluated using hypothesis tests such as t-tests or ANOVA. Therefore, the correct application of a scatter diagram is to demonstrate relationships between variables, making option B correct.
A political ballot gives voters the option to vote for one of three candidates. Eight voters cast their ballots.
Which statistical rule should be used to determine the possible voting outcomes?
Answer : A
The multiplication principle is used to determine the number of possible outcomes when multiple independent choices occur in sequence. In data-driven decision making and probability theory, this rule applies when each event has a fixed number of outcomes and each outcome is independent of the others.
In this scenario, each of the eight voters can independently choose one of three candidates. The total number of possible voting outcomes is calculated by multiplying the number of choices available for each voter. Because the voters act independently and order matters in counting outcomes, the multiplication principle is the correct method.
Conditional probability applies when outcomes depend on prior events, Bayes' theorem updates probabilities based on new information, and combinations are used when order does not matter. None of these fit the structure of this problem.
Therefore, the correct answer is A, multiplication principle.
Which two statements describe Ishikawa's seven basic tools of quality?
Choose 2 answers.
Answer : A, C
Ishikawa's seven basic tools of quality were designed to be simple, visual, and accessible. In data-driven decision making, these tools help employees identify, analyze, and solve quality problems without requiring advanced statistical expertise.
The tools---such as flowcharts, histograms, Pareto charts, and cause-and-effect diagrams---represent processes graphically, making patterns and issues easier to understand. Additionally, they are intentionally designed so that an average worker can easily understand and use them, supporting organization-wide quality improvement.
They do not rely on photographic representations, nor are they intended for advanced or expert-level training. Instead, they empower frontline employees to participate in continuous improvement efforts.
Therefore, the correct answers are A and C.
What results from starting an analysis with flawed data?
Choose 2 answers.
Answer : B, D
Starting an analysis with flawed data significantly undermines the effectiveness of data-driven decision making. One major consequence is that more time is spent managing data than analyzing data. Analysts must devote substantial effort to cleaning, validating, and correcting errors before meaningful analysis can occur, delaying insights and increasing costs.
Another critical result is that missing data tend to skew the results of the analysis. Incomplete data can distort averages, trends, and statistical relationships, leading to biased conclusions and unreliable decisions. This is especially problematic in predictive and inferential analytics, where assumptions about data completeness are essential.
Using spreadsheets or placing data in charts does not inherently result from flawed data, nor does it resolve data quality issues. While visualization can help identify errors, it is not a direct outcome of starting with flawed data.
Data-driven decision making emphasizes that poor-quality input leads to poor-quality output. Ensuring data accuracy and completeness before analysis is essential for producing valid insights. Therefore, the correct answers are B and D.