1.01 Analysing and classifying data

State whether the following are examples of univariate data or bivariate data:

Classify the following examples of data as either:

• Numerical discrete

• Numerical continuous

• Categorical nominal

• Categorical ordinal

Find the mode of the following scores:

2, 2, 6, 7, 7, 7, 7, 11, 11, 11, 13, 13, 16, 16

A rating system of 1 - 3 was used in a survey to determine the usefulness of a new feature. The ten scores shown below are known to have a mode of 1.

Find the missing score, x.

Find the median of 7, 4, 6, 3.

A set of 69 scores is arranged in ascending order. In what position does the median score lie?

In a set of 152 scores, between which two scores does the median lie?

The adjacent stem and leaf plot shows the prices, in dollars, of concert tickets locally and internationally:

Find the mean of the following sets of scores:

The following five numbers have a mean of 11:

11, 13, 9, 13, 9

If a new number is added that is smaller than 9, will the mean will be higher or lower?

Find the range of the following sets of scores:

Durations of calls (in minutes) made in a household were recorded as follows:

5,\text{ }\text{ } 11,\text{ }\text{ } 3,\text{ }\text{ } 9,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 5,\text{ }\text{ } 14,\text{ }\text{ } 14,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 7,\text{ }\text{ } 5,\text{ }\text{ } 3,\text{ }\text{ } 3,\text{ }\text{ } 7,\text{ }\text{ } 14,\text{ }\text{ } 5

A real estate agent wanted to determine a typical house price in a certain area. He gathered the selling price of some houses (in dollars):

317\,000, \text{ }\text{ }320\,000,\text{ }\text{ } 347\,000,\text{ }\text{ } 360\,000,\text{ }\text{ } 378\,000,\text{ }\text{ } 395\,000,\text{ }\text{ } 438\,000,\text{ }\text{ } 461\,000,\text{ }\text{ } 479\,000,\text{ }\text{ } 499\,000

Susanah has been growing watermelons. The weights of the watermelons (in kilograms) are: 15,\text{ }\text{ } 6,\text{ }\text{ } 5,\text{ }\text{ } 2,\text{ }\text{ } 4,\text{ }\text{ } 4,\text{ }\text{ } 5

The median house price in Humbleton is \$950\,000 with a mean price of \$1\,000\,000, and the median house price in Brockway is \$950\,000 with a mean price of \$880\,000.

Which town is most likely to have some very expensive houses? Explain your answer.

The selling price of recently sold houses are given:

\$467\,000, \$413\,000, \$410\,000, \$456\,000, \$487\,000, \$929\,000

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?

Marge grows two different types of bean plants. She records the number of beans that she picks from each plant for 10 days. Her records are as follows:

• Plant A: 4,\text{ } 4, \text{ }5, \text{ }7, \text{ }10,\text{ } 3,\text{ } 3,\text{ } 9,\text{ } 10

• Plant B: 8,\text{ } 7,\text{ } 5,\text{ } 5,\text{ } 9,\text{ } 7,\text{ } 8,\text{ } 7,\text{ } 5,\text{ } 6

The beaks of two groups of birds are measured, in millimetres, to determine whether they might be of the same species:

Two English classes, each with 15 students, sit a ten question multiple choice test. Their class results, out of 10, are below:

10 participants had their pulse measured before and after exercise with results shown in the adjacent stem and leaf plot:

Consider the frequency distribution table below:

Consider the following set of scores:

13, \text{ }15,\text{ } 5, \text{ }16,\text{ } 7,\text{ } 20,\text{ } 12

Consider the following set of scores:

- 3,\text{ } - 3,\text{ } 1,\text{ } 9,\text{ } 9,\text{ } 6,\text{ } - 9

There is a test to measure the Emotional Quotient (EQ) of an individual. Below are the EQ results for 21 people, listed in ascending order:

92,\text{ } 94,\text{ } 100,\text{ } 103,\text{ } 103,\text{ } 105,\text{ } 105,\text{ } 109,\text{ } 110,\text{ } 113, \text{ } 114,

114,\text{ } 116,\text{ } 118,\text{ } 118,\text{ } 119,\text{ } 120,\text{ } 125,\text{ } 125,\text{ } 126,\text{ } 130

Consider the following set of scores:

10,\text{ } 11,\text{ } 12,\text{ } 13,\text{ } 15,\text{ } 17, \text{ }19,\text{ } 20

Within what range do the middle 50\% of scores lie?

In competition, a diver must complete 8 rounds of dives. Her scores for the first 7 rounds are given below:

7.3,\text{ } 7.4,\text{ } 7.7,\text{ } 8.4,\text{ } 8.7,\text{ } 8.9,\text{ } 9.4

Determine her score in the 8th round if the upper quartile of all 8 scores is 8.85.

Consider the dot plot below:

A set of data has a five-number summary as shown in the table:

A group of Year 12 students were asked how many hours they spend on Hashtagram per day. The results are given below:

1.9, 1.1, \text{ }2.4, 2.3, \text{ }2.1, 1.2, \text{ }1.3, 1.6, \text{ }1.5, 1.8

The glass windows for an airplane are cut to a certain thickness, but machine production means there is some variation. The thickness of each pane of glass produced is measured (in millimetres) and the results are shown in the following dot plot:

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.

The mean income of people in Finland is \$45\,000. This is the same as the mean income of people in Canada. The standard deviation of Finland is greater than the standard deviation of Canada. In which country is there likely to be the greatest difference between the incomes of the rich and poor?

Consider the histogram below:

a

Find the range of the data set.

b

Find the mean of the data set. Round your answer to two decimal places.

c

Find the population standard deviation. Round your answer to two decimal places.

The scores of five diving attempts by a professional diver are recorded below:

5.6,\text{ } 6.6,\text{ } 6.3,\text{ } 5.9,\text{ } 6.4

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,\text{ } 18,\text{ } 20.5,\text{ } 21,\text{ } 21,\text{ } 21, \text{ }21.5, \text{ }22, \text{ }22,\text{ } 24,\text{ } 24,\text{ } 25,\text{ } 26,\text{ } 27

Consider the following table:

Consider the following table:

Consider the following table:

State whether the data in each graph is positively skewed, negatively skewed or symmetrical:

a

b

c

d

e

	Leaf
1	6\ 7\ 7
2	2\ 2\ 2\ 2\ 3\ 3\ 3
3	3\ 3\ 3\ 6\ 6\ 6\ 7\ 7\ 7\ 7\ 7
4	4\ 4\ 4\ 4\ 4\ 4
5	7\ 7

Key: 1 \vert 6 = 16

f

The following stem and leaf plot displays the ages of people who entered through the gates of a concert in the first 5 seconds:

VO_{2} Max is a measure of how efficiently your body uses oxygen during exercise. The more physically fit you are, the higher your VO_{2} Max. A group of people had their VO_{2} Max measured, the results are given below:

21,\text{ } 21,\text{ } 23,\text{ } 25,\text{ } 26,\text{ } 27,\text{ } 28,\text{ } 29,\text{ } 29,\text{ } 29,\text{ } 30,\text{ } 30,\text{ } 32,\text{ } 38,\text{ } 38,\text{ } 42,\text{ } 43,\text{ } 44,\text{ } 48,\text{ } 50,\text{ } 76