7.01 Standard deviation

Find the population standard deviation of the following sets of scores, correct to two decimal places:

Find the sample standard deviation of the following sets of scores, correct to two decimal places:

The table shows the number of goals scored by a football team in each game of the year:

Meteorologists predicted a huge variation in temperatures throughout the month of April. The temperature each day for the first two weeks of April were recorded as follows:16, \, 18, \, 20.5, \, 21, \, 21, \, 21, \, 21.5, \, 22, \, 22, \, 24, \, 24, \, 25, \, 26, \, 27

The scores of five diving attempts by a professional diver are recorded below:5.6, \, 6.6, \, 6.3, \, 5.9, \, 6.4

Han, a cricketer, has achieved scores of 52, 20, 68, 70 and 150 in his first five innings this season. In his sixth innings, he scores a duck or 0. Describe how this score in the sixth innings affected the following:

A batsman’s mean number of runs is 62 and the standard deviation is 13. In the next match, he makes 50 runs.

Explain how this latest match affects his mean and standard deviation.

The trial times (in seconds) of a female athlete for the 100\text{ m} sprint are recorded below:

11.0,\, 10.5,\, 12.2,\, 11.2,\, 11.6,\, 11.7,\, 10.8,\, 12.1,\, 11.0,\, 10.9

Seven millionaires with an average net wealth of \$41 million and a standard deviation of \$7 million are having a party. Suddenly Carlos Slim, who has a net wealth estimated to be \$31 billion, walks into the room.

The mean income of people in Country A is \$19\,069. This is the same as the mean income of people in Country B. The standard deviation of Country A is greater than the standard deviation of Country B. In which country is there likely to be the greatest difference between the incomes of the rich and poor?

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 \text{ m} sprints and the time to complete 50 sprints were recorded. The mean and standard deviation for the sprints are shown below:

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

What can we say about the comparison of their means and standard deviations?

The scores obtained by two classes are given below:

• Red class: \,48,\, 56,\, 49,\, 43,\, 41,\, 44,\, 49,\, 46

• Blue class: \,64,\, 52,\, 43,\, 69,\, 66,\, 65,\, 58,\, 42

The table shows the heart rate data of a group of people after exercise:

Consider the following pair of data sets below.

• 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 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

Compare the performance of the two brands of batteries.

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

Compare the wait times of the two companies.

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

• Pauline: 10,\, 31,\, 23,\, 6,\, 5,\, 38,\, 18,\, 19,\, 15,\, 21

• Dave: 52,\, 51,\, 77,\, 40,\, 61,\, 53,\, 60,\, 81,\, 52,\, 82

Compare the performance of the two players.