15.10 Comparisons using standard deviation

Consider the test results for four Geography classes, labelled as Class W, Class X, Class Y and Class Z:

Rank the classes from largest standard deviation to smallest standard deviation.

The mean income of people in Canada is \$43\,000. This is the same as the mean income of people in Germany. The standard deviation of Canada is greater than the standard deviation of Germany.

In which country is there likely to be the greatest difference between the incomes of the rich and poor?

Consider the following data sets:

• Set A: \, 2,\, 4,\, 5,\, 8,\, 8,\, 9,\, 9,\, 9,\, 10,\, 10,\, 10,\, 11,\, 12,\, 15

• Set B: \ 2,\, 2,\, 3,\, 4,\, 5,\, 5,\, 6,\, 7,\, 9,\, 11,\, 13,\, 13,\, 14,\, 15

The scores obtained by two classes are given below:

• Red Class: \, 55,\, 57,\, 49,\, 58,\, 68,\, 57,\, 60,\, 53,\, 56,\, 51

• Blue Class: \ 53,\, 59,\, 52,\, 49,\, 59,\, 49,\, 58,\, 57,\, 48,\, 54

Two companies record the wait time for calls to their customer hotlines over 10 calls. The recorded values are given below in minutes:

• Company X: \, 3.1,\, 2.1,\, 3.1,\, 3.2,\, 3.0,\, 2.6,\, 3.8,\, 2.7,\, 2.5,\, 3.5
• Company Y: \, 2.2,\, 3.1,\, 3.0,\, 2.5,\, 3.0,\, 3.2,\, 3.2,\, 2.7,\, 2.5,\, 2.5

The life of two brands of batteries are tested using a sample of 10 batteries from each brand. Their battery lives (in hours) are shown below:

• Brand X: \, 23.3,\, 19.7,\, 20.7,\, 25.3,\, 22.5,\, 19.1,\, 20.0,\, 20.7,\, 20.7,\, 20.9
• Brand Y: \, 23.2,\, 27.5,\, 25.0,\, 24.5,\, 22.7,\, 29.8,\, 22.9,\, 26.0,\, 26.4,\, 22.6

Two machines A and B are producing chocolate bars with the following mean and standard deviation for the weight of the bars:

Two friends compete in triple jump and the distance of 20 jumps were recorded. The mean and standard deviation for the jumps are shown below:

Two friends compete in 100 m sprints and the time to complete 50 sprints were recorded. The mean and standard deviation for the sprints are shown below.

Points scored by two friends over 10 rounds of a game are displayed below:

• Georgia: \, 10,\, 31,\, 23,\, 6,\, 5,\, 38,\, 18,\, 19,\, 15,\, 21
• Mario: \, 52,\, 51,\, 77,\, 40,\, 61,\, 53,\, 60,\, 81,\, 52,\, 82

Two cricketers compare the mean and standard deviation of their runs made per match. They conclude that Ivan is a more consistent batter but Bianca generally scores more runs per match.

Compare the mean and standard deviation of the two players.

Seven millionaires with an average net wealth of \$41 million with a standard deviation of \$8 million are having a party. Suddenly Warren Buffet, who has a net wealth estimated to be \$34 billion, walks into the room.

Luke, a cricketer, has made scores of 51, 25, 99, 35 and 90 in his first five innings this season. In his sixth innings, he scores a duck or 0. Describe how this new score affected the following: