Statistic and Probability

Question

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

You need to put the data in order so you can do a), b) and c)

a) 0 | will contain all numbers less than 10

1 | will contain ones digit for all numbers between 10 and 19

2 | will contain ones digit for all numbers between 20 and 29

The stem and leaf plot will have a shape that can be symmetric, skewed left (thick left tail) or right (thick right tail)

b) The mean is computed by summing the data values and dividing by the number of values (30)

Compute x = n+1 / 2, where is the n is the sample size = 30. so x = 15.5. In this case the median is the average of the 15th and 16th ordered values.

the mode is the most often occurring value - has to appear more than once - if more than one value appears an equal amount of times, then there are multiple modes.

c) if the mode > median > mean, then the distribution is skewed left (thick left tail)

if the mean < median > mode, then the distribution is skewed right (thick right tail)

if the mean, median and mode are approximately equal, then the distribution is symmetric