Question

Countable: For each of the following, categorize the nature of the data using one of these three descriptions:

(1) discrete because the number of possible values is finite;

(2) discrete because the number of possible values is infinite but countable;

(3) continuous because the number of possible values is infinite and not countable.

a. Exact lengths of the feet of members of the band the Monkees

b. Shoe sizes of members of the band the Monkees (such as 9, 9½, and so on)

c. The number of albums sold by the Monkees band

d. The numbers of monkeys sitting at keyboards before one of them randomly types the lyrics for the song “Daydream Believer.”

Short answer

a. The length of the feet of the band members is (3) continuous as the number of possible values is infinite and uncountable.

b. The different shoe sizes of the band members are (1) discrete because the number of possible values is finite.

c. The number of albums sold is (1) discrete because the number of possible values is finite.

d. The number of monkeys sitting at keyboards is (2) discrete because the number of possible values is infinite but countable.

Step-by-step solution

Given information

Four different descriptions of data are given related to the band Monkees. Also, three different categories are provided, using which the classification of the given four statements needs to be done.

Classification of data according to countability

Numerical data is categorized into two types:

Discrete data: Countable variables are classified under discrete data. These can hold specific integral values. Data can be finite or infinite. For example, the number of fruits in a basket (finite discrete data) and the number of trees in a dense forest (infinite discrete data).

Continuous data: Uncountable variables are classified under continuous data. These can hold any real value. They are infinitely many and can only be measured. For example, the mass of a body can only be measured on a scale.

 Step 3: Identification of the correct category 

a. As the length of feet can only be measured (not counted), it is categorized ascontinuous data.

b. As shoe sizes can hold specific discrete values and are finite in number, they are categorized as finite discrete data.

c. As the number of albums sold can be counted and are finite in number, they are categorized underfinite discrete data.

d. As the number of band members who have worked before producing a particular song can be infinitely large and countable, they are categorized as infinite discrete data.