Answer to Question #158482 in Statistics and Probability for paladin

Question

Question 5

The number of items rejected daily by a manufacturer because of defects for the last 30 days are:

20, 21, 8, 17, 22, 19, 18, 19, 14, 17, 11, 6, 21, 25, 4, 19, 9, 12, 16, 16, 10, 28, 24, 6, 21, 20, 25, 5, 17, 8

 

a)     Construct a stem-and-leaf display. What can conclude based on the display?        (7 marks)

b)     Calculate the mean, median, and mode of the data.                                                 (6 marks)

c)     Based on the answers in (b), make a conclusion about the skewness of the data.  (3 marks)

Answer 1

a) Stem| Leaf

0 | 4 5 6 6 8 8 9

1 | 0 1 2 4 6 6 7 7 7 8 9 9 9

2 | 0 0 1 1 1 2 4 5 5 8

The distribution is unimodal and bell shaped.

b) Mean$=\frac{478}{30}=15.93.$

Median$=\frac{17+17}{2}=17.$

There is no mode.

c) Since Mean<Median, the distribution is skewed left (negatively).