A quality control engineer records the diameters (in mm) of ball bearings from a production line. The data, representing a sample of ball bearings, is grouped into class intervals as follows:
– 9.5 – 9.7 mm: 4
– 9.7 – 9.9 mm: 6
– 9.9 – 10.1 mm: 5
(a) Calculate the estimated mean and standard deviation of the ball bearing diameters using the midpoint method.
(b) Based on your calculations in part (a), evaluate the reliability of the ball bearing production process in maintaining consistent diameters. Comment on what the standard deviation indicates about the consistency of the ball bearings.
Question
Calculate the estimated mean and standard deviation of the ball bearing diameters using the midpoint method with the provided grouped data. State your answers to two decimal places for the mean and two significant figures for the standard deviation.
Hint
Hint
Hint
Determine the midpoints for each interval, then apply the formulas for the mean and standard deviation of grouped data. Ensure you use the correct number of decimal places and significant figures as specified.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
Estimated mean ≈ 9.81 mm, estimated standard deviation ≈ 0.16 mm.
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Answer Explanation
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Question
Based on your calculations from part (a), evaluate the reliability of the production process in maintaining consistent ball bearing sizes. Explain what the magnitude of the standard deviation, relative to the mean, suggests about the consistency.
Hint
Hint
Hint
Consider what a small standard deviation implies about the spread of the data around the mean. Relate this to the consistency of the ball bearing sizes in the production process.
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Answer
Answer
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Explanation
Explanation
- Formula Booklet
Complete Answer
The small standard deviation (approximately 0.16 mm) relative to the mean (approximately 9.81 mm) indicates that the ball bearing diameters are clustered closely around the mean. This suggests a high level of consistency and thus a reliable production process. A smaller standard deviation implies greater consistency.
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Answer Explanation
Answer Explanation
