Question

A quality audit of a bottling company showed the number of defective batches outside of the specification limits for a particular oil product. The grouped data shown in the table below indicated the number of b=defective items per unit of measurement:

Volume (ml) f
20 - < 25 1
25 - < 30 2
30 - < 35 8
35 - < 40 5
40 - < 45 3
45 - < 50 1

3.1 Complete the table under the given columns: (4)

CLASS LIMITS f CUM < f CLASS MARK (X) X f X - X ̅ (X - X ̅)2 (X - X ̅)2 f

3.2 Calculate the mean value. (2)

3.3 Calculate the standard deviation. (3)

3.4 Draw the less-than ogive graph.
Use your graph to determine the median value. (5)

3.5 Calculate the 80th percentile value. (3)

3.6 Use the values from 3.2 and 3.4 to comment on the nature if the distribution.
Give a reason for your answer.