Business Statistics Quiz: Descriptive Statistics For Dashboards
20 questions · exam conditions
0:00
Descriptive Statistics For DashboardsQuestion 1 of 20

A sales manager is reviewing a dashboard of daily revenue for the past month. On the final day of the month, the team closed an exceptionally large, one-time enterprise deal, representing more than ten times the typical daily revenue.

How will the inclusion of this final day's revenue figure impact the mean and median daily revenue metrics for the month displayed on the dashboard?

The mean revenue will increase substantially, while the median revenue will increase only slightly or not at all.
Both the mean and the median revenue will increase by a substantial and roughly equal amount.
The median revenue will increase substantially, while the mean revenue will increase only slightly.
The mean revenue will decrease due to the outlier, while the median revenue will remain stable.
← Back to quizzes

Business Statistics Quiz

Business Statistics Quiz: Descriptive Statistics For Dashboards

Practice Descriptive Statistics For Dashboards in Business Statistics with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Descriptive Statistics For Dashboards, giving you a quick way to practice the rules, question types, and explanations that matter most for Business Statistics.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

A sales manager is reviewing a dashboard of daily revenue for the past month. On the final day of the month, the team closed an exceptionally large, one-time enterprise deal, representing more than ten times the typical daily revenue.

How will the inclusion of this final day's revenue figure impact the mean and median daily revenue metrics for the month displayed on the dashboard?

  1. The mean revenue will increase substantially, while the median revenue will increase only slightly or not at all. (correct answer)
  2. Both the mean and the median revenue will increase by a substantial and roughly equal amount.
  3. The median revenue will increase substantially, while the mean revenue will increase only slightly.
  4. The mean revenue will decrease due to the outlier, while the median revenue will remain stable.
Explanation: The mean is sensitive to extreme values (outliers). The single large deal will significantly pull the average up. The median, which is the middle value of the sorted dataset, is robust to outliers. Since only one data point is changing, the middle value of the 30 or 31 days will shift by at most one position, resulting in a small or no change.

Question 2

A call center manager's performance dashboard displays metrics for two senior agents over the past quarter. Agent A and Agent B have nearly identical mean call handle times. However, the standard deviation for Agent A's handle time is 45 seconds, while for Agent B it is 110 seconds.

Based on this dashboard data, what is the most accurate conclusion the manager can draw about the agents' performance?

  1. Agent B is more efficient than Agent A because a higher standard deviation indicates a capacity to handle complex calls.
  2. Agent A provides a more consistent customer experience, making their performance more predictable for staffing and planning. (correct answer)
  3. The median call handle time for Agent B is likely much lower than Agent A's to balance the high standard deviation.
  4. Both agents are performing at the same level because their average handle times are the same.
Explanation: Standard deviation measures the dispersion or variability of data points around the mean. A lower standard deviation (Agent A) implies that the call handle times are more clustered around the average, indicating consistency and predictability. A higher standard deviation (Agent B) indicates wide variation, meaning some calls are very short and others are very long, which is less consistent.

Question 3

A business analyst is preparing a summary of employee tenure for a corporate dashboard. After analyzing the data, they find the mean employee tenure is 8.5 years, while the median tenure is 5.2 years.

Given the relationship between the mean and median tenure, what is the most likely conclusion about the company's workforce composition?

  1. The data is left-skewed, indicating that the company has a large number of employees with very short tenures.
  2. The data is symmetric, suggesting an even distribution of employees across all tenure lengths.
  3. The data is right-skewed, indicating the presence of a group of long-tenured employees pulling the average up. (correct answer)
  4. The mean is higher than the median, which suggests a data entry error in the tenure records.
Explanation: When the mean is significantly greater than the median, the distribution is typically right-skewed (or positively skewed). This indicates that there is a long tail on the right side of the distribution, which in this context represents a number of employees with very long tenures (outliers) that inflate the mean relative to the median.

Question 4

A retail chain's operations dashboard shows that over the last six months, the mean number of items per transaction has remained stable at 4.0. However, the standard deviation has increased from 1.5 to 3.0 during the same period.

What is the most likely business implication of this change shown on the dashboard?

  1. Customers are, on average, buying more items per transaction than they were six months ago.
  2. The median number of items per transaction has most likely decreased significantly.
  3. The total number of transactions has decreased, leading to higher variability in the data.
  4. Customer purchasing behavior has become more polarized, with more 'small basket' and 'large basket' shoppers. (correct answer)
Explanation: A stable mean indicates the average has not changed. A significant increase in standard deviation means the data points are more spread out from the mean. In this context, it suggests fewer people are buying the average number of items (4), and more people are buying either very few items (e.g., 1) or many items (e.g., 7 or 8), leading to polarization and higher variability.

Question 5

A dashboard monitoring a website's page load times displays data for seven consecutive user sessions. The times, in seconds, are sorted as: 2.1, 2.4, 2.5, X, 3.5, 3.8, 8.7. The dashboard calculates and displays a median load time of 3.1 seconds for this period.

Given that the median is 3.1 seconds, what is the value of the missing data point X, and what is the mean load time for this sample?

  1. X = 3.1 seconds; the mean is approximately 3.73 seconds. (correct answer)
  2. X = 3.1 seconds; the mean is 3.10 seconds.
  3. X = 3.0 seconds; the mean is approximately 3.69 seconds.
  4. X cannot be determined; the mean is therefore also unknown.
Explanation: In a sorted dataset of 7 items, the median is the 4th value. Since the reported median is 3.1 and the list is sorted, X must be 3.1. The complete dataset is {2.1, 2.4, 2.5, 3.1, 3.5, 3.8, 8.7}. To find the mean, sum the values and divide by 7: (2.1+2.4+2.5+3.1+3.5+3.8+8.7)/7=26.1/7≈3.73(2.1+2.4+2.5+3.1+3.5+3.8+8.7) / 7 = 26.1 / 7 \approx 3.73 seconds.

Question 6

A quality control dashboard for a manufacturing plant tracks the number of defects per batch. For the last 20 batches, the mean number of defects was 8.0 with a standard deviation of 2.5. Today, a new batch (the 21st) is produced and has exactly 8 defects.

How will adding this new data point to the dataset affect the mean and standard deviation displayed on the dashboard?

  1. The mean will remain the same, and the standard deviation will increase.
  2. The mean will increase, and the standard deviation will decrease.
  3. The mean will remain the same, and the standard deviation will decrease. (correct answer)
  4. Both the mean and the standard deviation will remain the same.
Explanation: Adding a new data point that is exactly equal to the existing mean will not change the mean. However, this new data point has a deviation of zero from the mean. This adds a zero to the sum of squared deviations while increasing the count of data points (n). This reduces the average squared deviation, thus decreasing the variance and the standard deviation.

Question 7

A dashboard for tracking monthly customer support tickets is populated from a manual entry form. For one month, the five regional ticket counts were {25, 30, 32, 38, 150}. It was later discovered that the '150' was a typo and should have been '50'.

How does correcting this single data entry error affect the monthly mean, median, and standard deviation displayed on the dashboard?

  1. The mean, median, and standard deviation will all decrease.
  2. The mean will decrease, but the median and standard deviation will increase.
  3. The mean and standard deviation will decrease, while the median will remain unchanged. (correct answer)
  4. Only the mean will change; the median and standard deviation will be unaffected.
Explanation: Original data sorted: {25, 30, 32, 38, 150}. Median is 32. Corrected data sorted: {25, 30, 32, 38, 50}. The median is still the middle value, 32. The correction removes a large outlier, which will lower the mean (from 55 to 35) and reduce the overall spread of the data, thus decreasing the standard deviation.

Question 8

An operations dashboard displays employee productivity scores for two shifts. The morning shift has 10 employees with a mean score of 85. The evening shift has 15 employees with a mean score of 80.

The manager wants to add a single KPI for the overall daily productivity to the dashboard. What is the combined mean score for all 25 employees?

  1. 82.5
  2. 82.0 (correct answer)
  3. 83.0
  4. Cannot be determined without individual employee scores.
Explanation: This requires calculating a weighted average, not a simple average of the means. The calculation is: (count1×mean1)+(count2×mean2)count1+count2\frac{(\text{count}_1 \times \text{mean}_1) + (\text{count}_2 \times \text{mean}_2)}{\text{count}_1 + \text{count}_2}. So, (10×85)+(15×80)10+15=850+120025=205025=82.0\frac{(10 \times 85) + (15 \times 80)}{10 + 15} = \frac{850 + 1200}{25} = \frac{2050}{25} = 82.0.

Question 9

A company is updating its performance review dashboard. As a company-wide morale booster, management decides to give every employee a flat 5-point increase to their annual performance score (which is on a 100-point scale).

How will this universal 5-point increase affect the mean, median, and standard deviation of the scores displayed on the dashboard?

  1. The mean will increase by 5 points, but the median and standard deviation will be unchanged.
  2. The mean, median, and standard deviation will all increase by 5 points.
  3. The mean and median will each increase by 5 points, but the standard deviation will remain unchanged. (correct answer)
  4. The effect cannot be determined without knowing the original distribution of scores.
Explanation: Adding a constant value to every data point in a set shifts the entire distribution. Measures of central tendency (mean and median) will increase by that constant amount. However, measures of spread or dispersion (like standard deviation and range) will remain unchanged because the distance between each data point and the mean remains the same.

Question 10

A dashboard at a coffee shop chain is used to monitor the amount of coffee dispensed by two models of automated machines. Both are calibrated to dispense 300ml. The dashboard shows:

  • Machine X: Mean = 300ml, SD = 2ml
  • Machine Y: Mean = 300ml, SD = 15ml

Given that overflowing cups result in waste and costly cleanup, and under-filled cups lead to customer complaints, what is the most critical conclusion from this dashboard?

  1. Both machines are performing acceptably because their average dispense amount is accurate.
  2. Machine Y has a significant consistency problem and should be prioritized for maintenance to reduce its high variability. (correct answer)
  3. Machine X is likely more profitable because its low standard deviation implies it uses less coffee over time.
  4. The data is flawed, as two machines with the same mean cannot have such different standard deviations.
Explanation: While both machines have an accurate mean, the standard deviation reveals their consistency. Machine Y's high SD (15ml) indicates that many cups are likely significantly under-filled or over-filled, leading to both waste and customer dissatisfaction. Machine X's low SD (2ml) indicates it is highly consistent and reliable. The key issue is the high variability of Machine Y.

Question 11

A project manager's dashboard displays statistics for the hours worked last week by a small team of three employees. The dashboard reports a mean of 40 hours and a median of 42 hours.

Which of the following sets of hours worked by the three employees is consistent with the statistics shown on the dashboard?

  1. 38, 40, 42
  2. 30, 40, 50
  3. 40, 42, 44
  4. 36, 42, 42 (correct answer)
Explanation: The correct set must satisfy two conditions. The mean must be 40, and the median must be 42. Let's check the options: A) Mean = (38+40+42)/3 = 40. Median = 40. (Incorrect median) B) Mean = (30+40+50)/3 = 40. Median = 40. (Incorrect median) C) Mean = (40+42+44)/3 = 42. Median = 42. (Incorrect mean) D) Mean = (36+42+42)/3 = 120/3 = 40. Median = 42. (Correct)

Question 12

A retail chain's analytics team is creating a dashboard to monitor customer satisfaction scores across 50 stores. The dashboard currently shows that the mean satisfaction score is 7.8 out of 10, with a standard deviation of 0.9. Store managers can view their individual store's performance relative to the company average.

If Store #23 has a satisfaction score of 6.2, and the dashboard needs to communicate this store's relative performance effectively, which interpretation should be prominently displayed?

  1. Store #23 is approximately 1.78 standard deviations below the mean, indicating significant underperformance (correct answer)
  2. Store #23 is performing 1.6 points below average and needs immediate attention
  3. Store #23 is in the bottom 4% of all stores based on normal distribution assumptions
  4. Store #23 has a satisfaction deficit of 20.5% compared to the company average
Explanation: When evaluating performance relative to a group, standardized scores (z-scores) provide the most meaningful interpretation because they show exactly how many standard deviations a value falls from the mean. This allows for precise comparison and statistical context. To find Store #23's z-score: z=6.2−7.80.9=−1.60.9=−1.78z = \frac{6.2 - 7.8}{0.9} = \frac{-1.6}{0.9} = -1.78 This means Store #23 performs 1.78 standard deviations below the company average, which represents significant underperformance that warrants attention. Answer A correctly identifies this standardized interpretation. Answer B states the raw difference (1.6 points below average) but lacks statistical context. While mathematically correct, raw differences don't indicate whether the gap is meaningful or how it compares to typical variation across stores. Answer C claims Store #23 is in the bottom 4%, but this misapplies normal distribution probabilities. A z-score of -1.78 corresponds to approximately the 4th percentile, meaning the store performs better than only 4% of a normal distribution. However, this assumes the satisfaction scores follow a normal distribution, which isn't established, and the interpretation focuses on percentile ranking rather than the standardized performance measure. Answer D calculates a percentage difference (20.5%) by comparing the deficit to the mean, but this business-style metric doesn't provide the statistical context needed for performance evaluation across multiple locations. Study tip: In business statistics, always look for z-scores when comparing individual performance to group averages. Z-scores provide standardized context that raw differences and percentages cannot match for statistical decision-making.

Question 13

An operations manager is reviewing a dashboard that tracks daily production output across three manufacturing shifts. The dashboard shows summary statistics for each shift's daily output over the past month (22 working days).

Day shift shows mean output of 485 units (SD = 45), evening shift shows mean of 445 units (SD = 23), and night shift shows mean of 380 units (SD = 67). For dashboard optimization, which shift requires the most management attention based on these statistics?

  1. Day shift, because it has the highest absolute variability in production output
  2. Evening shift, because its lower output combined with low variability suggests systematic underperformance
  3. Day shift, because the combination of high output and high variability indicates process instability
  4. Night shift, because it has both the lowest mean output and highest relative variability (correct answer)
Explanation: When evaluating operational performance across different units, you need to consider both absolute performance (mean output) and consistency (variability). While standard deviation shows absolute variability, the coefficient of variation (CV = SD/Mean) reveals relative variability, which is crucial for fair comparison across units with different output levels. Let's calculate the coefficient of variation for each shift: Day shift CV = 45/485 = 0.093 (9.3%), Evening shift CV = 23/445 = 0.052 (5.2%), and Night shift CV = 67/380 = 0.176 (17.6%). The night shift shows both the lowest mean output (380 units) and the highest relative variability (17.6%), indicating inconsistent performance at an already suboptimal level. Option A incorrectly focuses only on absolute variability without considering the production context. While day shift has the highest standard deviation (45), this represents only 9.3% relative variation. Option B misinterprets evening shift's low variability as problematic when it actually indicates consistent performance, even if output could be higher. Option C treats high output as negative when combined with variability, but day shift's relative variability is actually moderate and its high mean output is positive. Option D correctly identifies that night shift combines poor performance with high inconsistency, making it the priority for management intervention. Low output hurts productivity, while high relative variability suggests unpredictable processes that need stabilization. Study tip: Always calculate coefficient of variation when comparing variability across groups with different means—it reveals which unit truly has the most problematic inconsistency relative to its performance level.

Question 14

TechFlow Analytics is preparing a quarterly performance dashboard for their client's e-commerce platform. The dashboard will display key metrics for daily website conversion rates over the past 30 days. The data analyst has calculated that the mean conversion rate is 3.2%, the median is 2.8%, and the standard deviation is 1.4%.

Based on the given statistics, what can the dashboard designer conclude about the distribution of daily conversion rates, and what additional metric would be most valuable for executive decision-making?

  1. The distribution is left-skewed; adding the mode would provide the most complete picture for executives
  2. The distribution is right-skewed; adding the interquartile range would better show variability than standard deviation alone (correct answer)
  3. The distribution is approximately normal; adding confidence intervals around the mean would be most valuable
  4. The distribution is bimodal; adding the range would help executives understand the full spectrum of performance
Explanation: Since the mean (3.2%) is greater than the median (2.8%), the distribution is right-skewed, indicating some days with unusually high conversion rates. For dashboard purposes, the IQR would complement the standard deviation by showing the middle 50% of performance, which is less sensitive to outliers and more intuitive for executives than standard deviation alone.

Question 15

A procurement manager's dashboard tracks the price of a component from Supplier X over the last 50 orders. The metrics are: Mean Price = $10.00, Standard Deviation = $0.50. The company signs a new contract, and the 51st order is placed at a fixed price of $10.25.

How will adding this 51st data point of $10.25 affect the mean and standard deviation for Supplier X's price history on the dashboard?

  1. The mean will increase, and the standard deviation will also increase.
  2. The mean will decrease, and the standard deviation will decrease.
  3. The mean will increase, and the standard deviation will decrease. (correct answer)
  4. The mean will decrease, and the standard deviation will also increase.
Explanation: The new data point (10.25)isgreaterthanthecurrentmean(10.25) is greater than the current mean (10.00), so it will pull the mean up. To determine the effect on standard deviation, we compare the new point's distance from the mean to the existing SD. The new point is 0.25awayfromthemean,whichiswithinonestandarddeviation(0.25 away from the mean, which is within one standard deviation (0.50). Adding a point that is relatively close to the mean will reduce the overall dispersion of the data, causing the standard deviation to decrease.

Question 16

A logistics company wants to add a key performance indicator (KPI) to its executive dashboard to monitor on-time delivery. The goal is to reliably meet promised delivery dates for the vast majority of customers. The primary data tracked is 'days late,' where a negative number is early, 0 is on-time, and a positive number is late.

Which combination of descriptive statistics would be most effective on the dashboard to track performance against this specific goal?

  1. The mean and standard deviation, because they give a complete picture of average performance and its variability.
  2. The median and standard deviation, because the median shows the typical experience and is robust to extreme delivery delays. (correct answer)
  3. The mean and the median, because comparing them reveals the skewness of the delivery performance.
  4. The mode and the range, because they show the most common delivery outcome and the absolute worst-case scenario.
Explanation: The goal is to track the experience of the 'vast majority' of customers, making the median the best measure of central tendency as it is not skewed by a few extremely late deliveries. The standard deviation is crucial for measuring the consistency and reliability of the delivery process. A low SD means deliveries are predictably on time.

Question 17

A dashboard for an e-commerce site shows summary statistics for revenue per customer from two different ad campaigns. Both campaigns have the same mean revenue. However, Campaign A's median revenue is higher than its mean, while Campaign B's median revenue is lower than its mean.

Based solely on these descriptive statistics, which conclusion is most strongly supported?

  1. Campaign B attracted more high-value customers than Campaign A.
  2. The distribution of revenue for Campaign A is likely left-skewed, while Campaign B's is likely right-skewed. (correct answer)
  3. The standard deviation of revenue for Campaign A must be smaller than that of Campaign B.
  4. Campaign A was more profitable because its median customer generated more revenue than its average customer.
Explanation: The relationship between mean and median indicates skewness. When median > mean (Campaign A), the distribution is typically left-skewed, meaning a few low-value outliers are pulling the mean down. When median < mean (Campaign B), the distribution is typically right-skewed, meaning a few high-value outliers are pulling the mean up. This directly implies that Campaign B attracted a few very high-value customers, but B is the more precise statistical description.

Question 18

A global company's primary sales dashboard displays all figures in Euros (€). A new dashboard view is being created for the US office, which requires all metrics to be converted to US Dollars ($). The fixed conversion rate used is €1.00 = $1.10.

If the previous month's mean daily sales were €50,000 with a standard deviation of €5,000, what will the new mean and standard deviation be in US Dollars on the new dashboard view?

  1. Mean of $55,000 and standard deviation of $5,000
  2. Mean of $50,000 and standard deviation of $5,500
  3. Mean of $55,000 and standard deviation of $6,050
  4. Mean of $55,000 and standard deviation of $5,500 (correct answer)
Explanation: When every data point in a dataset is multiplied by a constant c, the mean is multiplied by c and the standard deviation is also multiplied by c. Here, c=1.10c = 1.10. New Mean = (€50,000 \times 1.10 = 55,000\). New Standard Deviation = \(€5,000 \times 1.10 = 5,500).

Question 19

A dashboard displays response times for IT support tickets. The data is known to be right-skewed due to a few complex tickets that take a very long time to resolve. The current dashboard shows: Mean = 48 hours, Median = 36 hours. An analyst proposes displaying a '10% trimmed mean' (where the fastest 5% and slowest 5% of response times are removed before calculating the average) to better represent a typical ticket's resolution time.

After applying this trim, how would the new trimmed mean most likely compare to the original mean and median?

  1. The trimmed mean will be lower than the original mean but still higher than the original median. (correct answer)
  2. The trimmed mean will be higher than the original mean because outliers are removed.
  3. The trimmed mean will be lower than the original median because of the right-skewed distribution.
  4. The trimmed mean will be exactly equal to the original median, creating a perfect measure of central tendency.
Explanation: The original data is right-skewed (Mean > Median), meaning the mean is inflated by high-value outliers (long response times). Trimming the slowest 5% will remove these outliers, causing the mean to decrease significantly. It will move closer to the median. However, it is unlikely to fall below the median because the skew often persists even in the trimmed data. Therefore, the trimmed mean will be between the original median and the original mean.

Question 20

A marketing campaign dashboard is designed to show the number of leads generated each day over a 5-day work week. The dashboard is programmed to show a running weekly mean. After Day 4, the mean is 100 leads per day. The lead counts for the first four days were 90, 95, 105, and 110.

After the data for Day 5 is entered, the final 5-day mean is updated to 100. What was the number of leads on Day 5, and how does the 5-day median compare to the 5-day mean?

  1. Day 5 leads were 100; the median is 100, which is equal to the mean. (correct answer)
  2. Day 5 leads were 100; the median is 105, which is higher than the mean.
  3. Day 5 leads were 102; the median cannot be determined from the information given.
  4. Day 5 leads were 100; the median is 95, which is lower than the mean.
Explanation: First, calculate the leads for Day 5. If the 5-day mean is 100, the total leads must be 5×100=5005 \times 100 = 500. The sum of the first four days is 90+95+105+110=40090 + 95 + 105 + 110 = 400. Therefore, Day 5 must have had 500−400=100500 - 400 = 100 leads. Second, find the median of the complete 5-day dataset: {90, 95, 100, 105, 110}. The middle value (the 3rd value) is 100. Thus, the median is 100, which is equal to the mean.