To find the mean, median, and mode of the given data set, we first need to list the times recorded in seconds:
Data set: 55, 52, 74, 64, 67, 60, 48, 48
Step 1: Calculate the Mean
To calculate the mean, add all the values together and then divide by the number of values.
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Sum of the values: \( 55 + 52 + 74 + 64 + 67 + 60 + 48 + 48 = 448 \)
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Number of values: There are 8 values.
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Mean: \[ \text{Mean} = \frac{\text{Sum of values}}{\text{Number of values}} = \frac{448}{8} = 56 \]
Step 2: Calculate the Median
To find the median, we need to order the values from least to greatest and then find the middle value.
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Ordered data set: 48, 48, 52, 55, 60, 64, 67, 74
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Since there are 8 values (an even number), the median will be the average of the 4th and 5th values.
- 4th value: 55
- 5th value: 60
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Median: \[ \text{Median} = \frac{55 + 60}{2} = \frac{115}{2} = 57.5 \]
Step 3: Calculate the Mode
The mode is the value that appears most frequently in the data set.
- In this case, the value 48 appears twice while all other values appear only once.
Summary of statistics:
- Mean: 56
- Median: 57.5
- Mode: 48
Interpretation
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Mean (56): This suggests that, on average, students perceive the time as slightly less than 1 minute (60 seconds).
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Median (57.5): The middle value supports that most students felt the time was short but not excessively so.
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Mode (48): The most common response being 48 seconds suggests some students significantly underestimated the 1 minute duration.
From these statistics, we can conclude that students generally underestimated the 1 minute duration, as both the mean and mode are below 60 seconds. This might suggest that students have a tendency to perceive time as passing faster than it actually does in this context or that they were not fully attentive during the timing.