STATISTICS ASSIGNMENT

Statistics Assignment

Statistics Assignment

Question No. 1 (a)

The five number summary includes five items: sample minimum, lower quartile, median, upper quartile, and sample maximum. Calculating five number summary of the following observations:

16, 26, 17, 11, 24, 25, 19, 14, 9, 2, 23, 30, 23, 56, 18, 49, 12, 29

Putting data in order:

2, 9, 11, 12, 14, 16, 17,18,19,23,23,24,25, 26, 29, 30, 49, 56

The minimum and maximum values

The minimum and maximum values of the observations are 2 and 56 respectively.

Lower and Upper Quartile

Lower quartile =

1 (n + 1)

4

=

1 (18 + 1)

4

=

19

4

=

4.75 th

Lower quartile=

x + 0.75x

=

(12) + 1.5

=

13.5

Upper quartile =

3 (n + 1)

4

=

3(18 + 1)

4

=

57

4

=

14.25 th

Upper quartile=

x + 0.25x

=

(26) + 0.75

=

26.75

Median

The median of the observation is the number that comes in the middle of the middle two numbers of the observation, which are 19 and 23.

Median =

19 + 23

2

=

42

2

=

21

Five Number Summary

Sample minimum = 2

Lower quartile =13.5

Median=21

Upper quartile=26.75

Sample maximum= 56

Question No. 1 (b)

Box Plot

The box plot is a diagram that represents the five number summary. The box plot provides us the following information. The whiskers show that the lowest emission is 2 tons and the highest is 56 tons. This means the range of the data is 54. The points outside the whiskers, i.e. 49 tons and 56 tons, are the outliers. An outlier is an observation that is numerically distant from the rest of the data. This means that two factories are emitting sulfur oxide at a very high rate. The line on the box plot shows the median of the data, which is 21 tons. The median 21 tons if the data is arranged from the least to greatest.

The value of lower quartile represent that one quarter of the data lies below 13.50 tons, i.e. one quarter of the factories emit sulfur oxide less than 13.50 ...