Data Detectives
This word means information collected through observations, measurements, or responses.
What is data?
Favorite school subject is an example of this type of data: categorical or numerical.
What is categorical data?
This collection method asks people questions and records their responses.
What is a survey?
This graph uses separate bars to compare categories, such as favorite school subjects.
What is a bar graph?
Find the mode: 2, 3, 3, 4, 5.
What is 3?
A data scientist begins by identifying a problem and asking one of these.
What is a question?
The number of books a student reads is an example of this type of data: categorical or numerical.
What is numerical data?
A school has 600 students, but researchers survey only 60. The 60 students are called this.
What is a sample?
You record the classroom temperature every hour. This graph is a good choice for showing how it changes over time.
What is a line graph?
Find the range: 4, 7, 9, 10, 15.
What is 11? Because 15 − 4 = 11.
A spreadsheet lists the same student’s survey response twice by mistake. Removing the extra entry is part of this process.
What is data cleaning?
A jersey number uses digits, but it identifies a player rather than measuring an amount. Is it categorical or numerical data?
What is categorical data?
To learn the favorite sport of all eighth graders, you survey only the basketball team. Explain the problem.
The sample is biased because basketball players may have different preferences from other eighth graders.
A transportation table shows: Bus—12 students; Car—8; Walk—5. How many students were surveyed?
What is 25 students?
Find the mean: 6, 8, 10, 12.
What is 9? Because 36 ÷ 4 = 9.
“Which lunch is best?” is vague. Rewrite it as a question that can be investigated by collecting data from eighth graders.
“Which school lunch do eighth graders choose most often?” Accept other measurable questions that identify the group and what will be measured.
The number of students on a bus is discrete numerical data. A student’s height is this other kind of numerical data.
What is continuous data?
Which method is more likely to represent the whole grade: surveying the first 20 friends you see or randomly selecting students from the full eighth-grade roster? Explain.
Randomly selecting students from the full roster, because it reduces the influence of friendship groups and gives each student a chance to be selected.
Two bars show 48 votes and 50 votes, but the vertical axis begins at 47. Explain how this could mislead a viewer.
It can make the two-vote difference appear much larger than it is.
Find the median: 3, 5, 7, 9, 12, 14.
What is 8? Average the two middle values: (7 + 9) ÷ 2.
Students who practice an instrument more often tend to earn higher music grades. Explain why this does not prove that practice alone caused the higher grades.
Other factors could affect grades, such as previous experience or extra lessons. A relationship does not by itself prove cause and effect.
A survey asks students to rate lunch as poor, fair, good, or excellent. Explain why these responses are categorical even though they have an order.
They describe categories with a meaningful order, rather than measured numerical amounts. These are ordered, or ordinal, categories.
A class investigates how students travel to school. Name two pieces of personal information it does not need to collect.
Examples: students’ full names, exact home addresses, phone numbers, or dates of birth. Accept any two unnecessary personal details.
A scatter plot shows that as daily screen time increases, hours of sleep tend to decrease. Name the direction of the relationship and describe it.
What is a negative association? Higher screen time tends to be associated with less sleep.
Five students report these reading times: 10, 12, 13, 15, and 100 minutes. Which better represents a typical reading time—the mean or median? Explain.
What is the median, 13 minutes? The unusually high value of 100 pulls the mean upward.