Consider the following data on lengths of 30 pieces of metal.

Question

18 26 15 17 7 27 24 17 10 17
23 29 28 18 10 23 16 6 12 26
5 12 23 22 24 14 16 26 19 22
a. Define an outlier. Give an example of an outlier from the above data set. [3]
b. (i) Calculate and interpret the: range, mean, mode and median of the lengths of metal pieces. [8]
(ii) Calculate the sample standard deviation of the above data set. [4]
(iii) Calculate and interpret the Lower quartile, the Second quartile, and the Upper quartile. [9]
(iv) Calculate the Inter-quartile range and the Semi-inter quartile range. [4]
(v) Calculate and interpret the 20th percentile and 85th percentile from the data set above. [6]

Answer 1

An outlier is a value that is much larger than the rest or much smaller than the rest.

range is the difference between the largest and the smalleest value.

mean = add them all and divide by 30

mode is the value that occurs more than once.

median. put all of the data in order from lowest to highest and find the middle number.

I hope you are allowed to use a statistical calculator because this would be a lot of work to do data piece by data piece.

The lower quartile is the is the lowest 1/4 of the data. You can actually find it by finding the middle between the lowest value and the median.
second quartile is just the median

Upper quartile is the upper 1/4 of the data find it by finding the value that is half way between the median and the largest number.

The interquartile range is the difference between the lower and upper quartiles.

20th percentile. 20% of the data falls below that point. 20% of 30 = 6 so it would be the bottom 6.

85% is the data below this point.

.85 x 30