Question

1. for each of the following, determine whether the question is a statistical question. give a reason for your answer.

a. how many letters are in my last name?
b. how many letters are in the last names of the students in my 6th grade class?
c. what are the colors of the shoes worn by the students in my school?
d. what is the maximum number of feet that roller coasters drop during a ride?
e. what are the heart rates of the students in a 6th grade class?
f. how many hours of sleep per night do 6th graders usually get when they have school the next day?
g. how many miles per gallon do compact cars get?

1. identify each of the following data sets as categorical (c) or numerical (n). explain your answer.

a. arm spans of 12 6th graders
b. number of languages spoken by each of 20 adults
c. favorite sport of each person in a group of 20 adults
d. number of pets for each of 40 3rd graders
e. number of hours a week spent reading a book for a group of middle school students

1. rewrite each of the following questions as a statistical question.

a. how many pets does your teacher have?
b. how many points did the high school soccer team score in its last game?
c. how many pages are in our math book?
d. can i do a handstand?

Explanation:

1. Determining statistical questions

A statistical question has variability in the answers.

a.

• The number of letters in one's own last - name is a single, non - variable value. So, it is not a statistical question.

b.

• Similar to a, it is about a single, definite value for a specific individual's last name, not a statistical question.

c.

• The last names of students in a 6th - grade class will vary, so this is a statistical question.

d.

• The colors of shoes worn by students in a school will vary among students, so it is a statistical question.

e.

• The maximum number of feet that roller coasters drop during a ride can be found by looking at multiple roller coasters, and there is variability among different roller coasters, so it is a statistical question.

f.

• The heart rates of students in a 6th - grade class will vary from student to student, so it is a statistical question.

g.

• The number of hours of sleep per night for 6th - graders on a school night will vary among 6th - graders, so it is a statistical question.

h.

• The miles per gallon that compact cars get will vary among different compact cars, so it is a statistical question.

Categorical data represents types or categories, while numerical data represents numbers that can be counted or measured.

a.

• Arm spans are measured in units (such as inches or centimeters), so it is numerical data (N).

b.

• The number of languages spoken is a countable number, so it is numerical data (N).

c.

• Favorite sport is a category (e.g., basketball, football), so it is categorical data (C).

d.

• The number of pets is a countable number, so it is numerical data (N).

e.

• The number of hours spent reading is a measurable number, so it is numerical data (N).

We need to rewrite the questions to account for variability in the data.

a.

• Instead of asking about one teacher, we can ask "How many pets do the teachers in our school have?"

b.

• Instead of asking about one game, we can ask "How many points did the high - school soccer team score in its last 10 games?"

c.

• Instead of asking about one math book, we can ask "How many pages are in the math books used by students in our school?"

d.

• Instead of asking about one person, we can ask "What percentage of students in our class can do a handstand?"

Answer:

a. Not a statistical question
b. Not a statistical question
c. Statistical question
d. Statistical question
e. Statistical question
f. Statistical question
g. Statistical question
h. Statistical question

2. Identifying data sets