The standard deviation measures the dispersion or spread of data points within a dataset. A smaller standard deviation indicates that the data points are clustered more closely around the mean (and often the median), suggesting greater consistency. A larger standard deviation indicates that the data points are more spread out, suggesting less consistency. Team Alpha has a standard deviation of 2 hours, which is much smaller than Team Beta's standard deviation of 10 hours. This indicates that the working hours of employees in Team Alpha are much more consistent and less varied than those in Team Beta. Why others are wrong: A — The median indicates the middle value, not the average (mean). We cannot infer a difference in average hours between the teams solely from their standard deviations. C — A larger standard deviation (Team Beta) suggests a wider range of values, making it more likely that extreme values (both high and low) would be observed in Team Beta, not Team Alpha. D — The median indicates that 50% of the data points are below it and 50% are above it. It does not provide information about the exact number of employees working precisely 40 hours, nor does it imply equality of such counts between teams.

List the sales figures: 65, 72, 68, 75, 63, 70, 68. Arrange the figures in ascending order: 63, 65, 68, 68, 70, 72, 75. There are 7 data points. The median is the middle value in an ordered set of numbers. For an odd number of data points (n), the median is the ((n+1)/2)th value. Here, n = 7, so the median is the ((7+1)/2) = 4th value. The 4th value in the ordered list (63, 65, 68, **68**, 70, 72, 75) is 68. Why others are wrong: B — This value is close to the mean (average), which is approximately 68.7, not the median. C — This would be the 5th value if sorted, or a result of an incorrect calculation or sorting error. D — This is the highest number of croissants sold, not the median.

1. First, remove the anomalous value (450 ms) from the dataset. The remaining data points are: 210, 225, 215, 230, 205, 220. 2. Arrange the remaining data points in ascending order: 205, 210, 215, 220, 225, 230. 3. Since there are 6 data points (an even number), the median is the average of the two middle values. 4. The two middle values are the 3rd and 4th values in the ordered list: 215 and 220. 5. Calculate their average: (215 + 220) / 2 = 435 / 2 = 217.5 ms. Why others are wrong: A — This would be the median if 215 were the sole middle value in an odd-numbered dataset, or if the average of the middle two values was miscalculated. C — This would be the median if 220 were the sole middle value in an odd-numbered dataset, or if the average of the middle two values was miscalculated. D — This is the largest value among the remaining data points before finding the median.

1. To find the median, first arrange the data points in ascending order: 18, 18, 19, 20, 21, 22, 25. 2. There are 7 data points (an odd number). 3. The median is the middle value, which is the ((n+1)/2)th value. 4. For n=7, the median is the ((7+1)/2) = 4th value. 5. Counting from the beginning of the ordered list, the 4th value is 20. Why others are wrong: A — This is the minimum temperature, not the median. B — This is the 3rd value in the ordered list, not the middle. D — This is the 5th value in the ordered list, not the middle.

Adding a constant value to every data point in a set shifts the entire distribution but does not change the spread or variability of the data. Standard deviation is a measure of the dispersion or spread of data points around their mean. If every data point increases by the same amount, the mean also increases by that same amount. Consequently, the distance of each data point from the new mean remains unchanged. Therefore, the standard deviation, which quantifies this spread, remains the same. Why others are wrong: B — Incorrectly assumes the constant value added to the data points is also added to the standard deviation. C — Incorrectly assumes the standard deviation becomes the value of the constant added to the data points. D — Incorrectly suggests a multiplicative effect or some other miscalculation based on the constant change.