E6010 diagnostic

What is the mean length (to 1 decimal place) of the 15 M6 bolts measured from the sample: {31.1, 30.7, 28.7, 31.3, 30.3, 31.2, 29.1, 30.6, 30.7, 31.1, 30.8, 30.0, 31.7, 29.5, 30.7}?

• 30.6 mm

• 30.9 mm

• 30.3 mm

• 31.0 mm

Which of the following is a suitable way to present the measurements of the 15 sampled M6 bolts (in mm) so that it is clear and easy for a non-statistician to understand?

• A bar chart showing the frequency of each measurement range (e.g., 28.5-29.4mm, 29.5-30.4mm, etc.)

• A complex statistical formula with all calculations shown

• A table with only the mean and standard deviation, without showing the actual data

• A scatter plot with unrelated variables

What conclusion can be drawn from analysing the measurements of the 15 sampled M6 bolts (lengths: 31.1, 30.7, 28.7, 31.3, 30.3, 31.2, 29.1, 30.6, 30.7, 31.1, 30.8, 30.0, 31.7, 29.5, 30.7) given the specification is 30mm ± 1mm?

• Most bolts are within the specified tolerance, but a few are outside the acceptable range.

• All bolts are exactly 30mm long as specified.

• None of the bolts meet the required length specification.

• The majority of bolts are shorter than the minimum allowed length.

What recommendations should you offer your Quality Manager based on the sample measurements of the M6 bolts (31.1, 30.7, 28.7, 31.3, 30.3, 31.2, 29.1, 30.6, 30.7, 31.1, 30.8, 30.0, 31.7, 29.5, 30.7) given the specification is 30mm ± 1mm?

• Investigate the cause of bolts outside the tolerance and improve quality control.

• No action is needed as all bolts are within specification.

• Increase the length specification to 32mm to accommodate all bolts.

• Reduce the sample size to avoid outliers.

What is the sample size (n) of bolts measured?

• 15 bolts

• 10 bolts

• 20 bolts

• 25 bolts

What is the sum of the bolt lengths in the sample?

• 457.5 mm

• 350 mm

• 500 mm

• 600 mm

What is the mean (average) length of the bolts?

• 30.5 mm

• 28.0 mm

• 32.0 mm

• 34.5 mm

What is the median (middle value) of the bolt lengths?

• 30.7 mm

• 28.5 mm

• 32.1 mm

• 29.9 mm

What is the sample standard deviation of the bolt lengths?

• ≈ 0.85 mm

• ≈ 0.45 mm

• ≈ 1.20 mm

• ≈ 0.30 mm

What is the minimum bolt length in the sample?

• 28.7 mm

• 32.5 mm

• 30.0 mm

• 35.2 mm