12.05 Spread of data

Find the range of the following sets of scores:

A group of students had a range in marks of 14 and the lowest score was 9. What was the highest score in the group?

The range of a set of scores is 8, and the highest score is 19. What is the lowest score in the set?

For each set of scores, find:

Consider the dot plot below:

Consider the data set below:9, \, 5, \, 6, \, 3, \, 9, \, 8, \, 4, \, 2, \, 3, \, 2Calculate:

Fred was told he was ranked in the 80th percentile for mathematics in an end of year exam. However, his teacher only posted a list of results, without names, as shown below:21, \, 29, \, 31, \, 33, \, 34, \, 42, \,46, \, 47, \, 49, \, 58, \, 61, \, 63, \, 65, \, 72, \, 76, \, 81, \, 84, \, 87, \, 91, \, 95

Consider the following data set containing 100 scores in a 10 \times 10 grid:

Charlie is in a table tennis league. He is ranked third out of 30 people. Calculate in what percentile his team lies.

Roald is in a volleyball competition. His team is ranked 46th out of 180 teams. Calculate in what percentile his team lies. Give your answer to the nearest whole number.

Use the statistics mode on the calculator to determine the standard deviation of the following sets of scores. Round your answer to two decimal places.

Consider the following table:

In a study, a group of people were shown 30 names, and after 1 minute, they were asked to recite as many names by memory as possible. The results are presented in the dot plot:

a

What does each dot represent?

b

How many people took part in the study?

c

What is the largest number of names someone remembered?

d

What was the smallest number of names someone remembered?

e

What is the range?

A cyclist measured his heart rate immediately after finishing each event in which he competed. The results are recorded in the following stem plot:

The graph shows the number of visa applications approved by an embassy each day over a period of time:

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?

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

Consider the following chart showing the range of heights for boys aged 10 to 18 years:

(Source: State Government of Victoria, Department of Education and Training)

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

Consider the following chart showing the range of heights for girls aged 10 to 18 years:

(Credit: State Government of Victoria, Department of Education and Training)

Rosey is aged 14 and is 160 \text{ cm} tall. What percentage of girls her age are shorter than her?

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

The scores obtained by two classes are given below:

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

• Blue Class: 53 ,\, 57 ,\, 62 ,\, 51 ,\, 56 ,\, 62 ,\, 58 ,\, 55 ,\, 58 ,\, 51

Seven millionaires with an average net wealth of \$41 million with 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.

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 0.