Jerome is a huge baseball fan. He loves to collect baseball cards. He has cards of all current and past players. Each card has a picture and information about the player. Jerome brought his baseball card collection to school and let the other students look at them.

A question is statistical if it can be answered with data that varies

Posing Statistical Questions

What is a Statistical Question?

Are the following questions statistical questions?

Some students asked:

How many cards do you have altogether?

What is the typical cost of a card in your collection?

Where did you get the cards?

Which of these questions do you think are statistical questions?

What do I mean by a "statistical question"?

1. How tall is your 6th grade teacher?

2. What is the hand span (measured from the tip

of the thumb to the tip of the small finger) of the

students in Ms. Majors class?

3. Who is my favorite movie star?

4. What are the favorite colors of the students in

Ms. Majors class?

5. How many brothers and sisters does my best

friend have?

$1.25

Monday, April 6, 2015

Vol XCIII, No. 311

**Types of Data**

Variability of Data

Which of these data sets would have the most variability?

Write down answers in your notebook.

1. Number of minutes students in Ms. Majors class spend getting ready for school

2. Number of pockets on the clothes in

Ms. Majors class

**Unit 4: Statistics**

Step 1:

Pose a question that can be answered by data.

Step 2:

Determine a plan to collect the data.

Step 3:

Summarize the data with graphs and numerical summaries.

Step 4:

Answer the question posed in Step 1 using the data and summaries.

What is a Statistical Question?

A statistical question is one that can be answered with data and for which it is anticipated that the data (information) collected to answer the question will vary.

How many cards do you have altogether?

What is the typical cost of a card in your collection?

Where did you get the cards?

The first question is

not

a statistical question because there is only one answer. The second and third questions are statistical because the answers could vary

Ask yourself: Will the data vary?

Write down answers in your notebook

Variability refers to how spread out the data is

. Commonly used measurements of variability include: range, median, variance and standard deviation.

Write some examples of both kinds of data in your notebook.

What are other types of categorical data?

What are other examples of numerical data?

There are two types of data: numerical and categorical. If we recorded the age of 25 baseball cards, we would have numerical data. If we recorded the team of the featured player for 25 baseball cards, we would have categorical data. Although you still have 25 data values, the data values are not numbers. They would be team names, which you could think of as categories

Suppose you collected data on the following. What are some of the possible values that you might get? Are these categorical or numerical?

Write your answers down in your notebook.

1. Eye color

2. Favorite TV show

3. Amount of rain that fell during a storm

4. High temperatures for each of 12 days

Practice

Identify each of the following data sets as categorical (c) or numerical (n).

Write your answers in your notebook.

1. Heights of 20 7th graders

2. Favorite flavor of ice cream for each of 10 7th graders

3. Hours of sleep on a school night for 30 7th graders

4. Type of beverage drank at lunch for 15 7th graders

5. Number of pencils in each locker of 15 7th graders

6. Grade in school of all of your cousins

7. Birth dates of 35 7th graders

Practice

For each of the following statistical questions, students asked Jerome to identify whether the data are numerical or categorical.

Explain your answer and list four possible data values in your notebook.

1. How old are the cards in the collection?

2. How much did the cards in the collection cost?

3. Where did you get the cards?

Check for Understanding

1. Indicate whether each of the following two questions is a statistical question. Explain why or why not in your notebook.

a. How much does Susan's dog weigh?

b. How much do the dogs belonging to students at our school weigh?

2. If you collected data on the weights of dogs, would the data be numerical or categorical? Explain how you know it is numerical or categorical in your notebook.

ANSWERS:

1. How tall is your 6th grade teacher?

Not statistical, you will only get one answer (possible answer: 5' 7"). The data does not vary.

2. What is the hand span (measured from the tip of the thumb to the tip of the small finger) of the students in Ms. Majors class?

Statistical, the answers will vary (possible answers: 19 cm, 18 cm, 19.5 cm, etc). The data varies.

3. Who is my favorite movie star?

Not statistical, you will only get one answer (possible answer: Marilyn Monroe). The data does not vary.

4. What are the favorite colors of the students in Ms. Majors class?

Statistical, the answers will vary (possible answers: blue, purple, yellow, etc). The data varies.

5. How many brothers and sisters does my best friend have?

Not statistical, you will only get one answer (possible answer: 2). The data does not vary.

NOTE:

You could easily change the non-statistical questions to a statistical question by modifying the question. For example, instead of asking "who is

MY

favorite movie star" one could ask "who is the favorite movie star of the

students in Liberty Public Schools

". This would gather data that varies and therefore be statistical.

ANSWERS

1. Number of minutes students in Ms. Majors class spend getting ready for school. This one would have the most variability. Think about all the different students in our class (boys, girls, those who just wake up and run out the door, those who take the time to curl their hair, etc). We would have students who get ready for school in as little as 10 minutes and those who take over an hour to get ready.

2. Number of pockets on the clothes in Ms. Majors class. This one would have the least variability. Most pants have 0 - 4 pockets on them and most shirts have 0 - 2 pockets on them. Most students would have the same amount of pockets with little variability.

Categorical

Values or observations that can

be sorted into groups or categories.

Examples: Sex, Eye color and Favorite color.

Bar charts and pie graphs are used to graph categorical data.

Numerical

Values or observations that can be measured. And these numbers can be placed in ascending or descending order.

Examples: Height, Arm Span and Weight.

Scatter plots and line graphs are used to graph numerical data.

Note

Zip codes would be categorical even

though they are numbers since

they would be grouped in

categories and not placed in ascending

or descending order.

Possible answers:

1.

Categorical

: brown, blue, hazel

2.

Categorical

: Friends, New Girl, Fresh off the Boat

3.

Numerical

: 1 in., 2.5 in., 0.4 in.

4.

Numerical

: 110, 105, 102, 98

Answers

1. n 4. c 7. c

2. c 5. n

3. n 6. c

A quick and easy way to decide whether data is numerical or categorical is to ask yourself “Can I calculate an average of these numbers?. If you can calculate an average, the data is numerical, if you cannot, the data is categorical. Since an average birth date or average year level has no meaning, this data is categorical, even though the data is presented as numerals. The same thing goes for zip codes.

Answers

1. n - examples would include: 7 years, 15 years, 2 weeks, etc. These numbers could be averaged to tell the general age of his collection.

2. n - examples would include: $3.50, $15.00, $26.25, etc. These numbers could be averaged to tell the average cost of his collection.

3. c - examples would include: Game Stop, Wal-Mart, Comicon, etc.

Answers

1. a. Not statistical. This question would result in one answer, so the data does not vary.

b. Statistical. This question would gather a lot of data that would vary so it is a statistical question.

2. The data would be numerical. You could use the data to find the average weight of all of the dogs.