Basics

Basic knowledge to test your knowledge in data distributions
👁 382
statistics
calculate
Questions #: 14
Time: 5 minutes
Pass Score: 80.0%
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Mode

You can learn and make use of numbers if you combine it with context

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Individuals and variables

  • are the objects described in a set of data. are sometimes people. When the objects that we want to study are not people, we often call them .
  • A  is any characteristic of an . A  can take different values for different .
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Individuals
cases
variable
individual
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Any set of data contains information about some group of (1)__________. The information is organized in (2)_________

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individuals
variables
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Data for students in a statistics class

The below figure shows part of a data set for students enrolled in an introductory statistics class. Each row gives the data on one student. The values for the different variables are in the columns. This data set has eight variables. ID is an identifier for each student. Exam1, Exam2, Homework, Final, and Project give the points earned, out of a total of 100 possible, for each of these course requirements. Final grades are based on a possible 200 points for each exam and the final, 300 points for
Homework, and 100 points for Project. Total Points is the variable that gives the composite score. It is computed by adding 2 times Exam1, Exam2, and Final, 3 times Homework plus 1 times Project. Grade is the grade earned in the course. This instructor used cut-offs of 900, 800, 700, etc. for the letter grades

  1. Give the values of the variables Exam1(1), Exam2(2), and Final(3) for the student with ID equal to 105
  2. A student whose data do not appear on the spreadsheet scored 88 on Exam1, 85 on Exam2, 77 for Homework, 90 on the Final, and 80 on the Project. Find Total Points(4) for this student and give the grade earned(5)

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Explanation

When you plan a statistical study or explore data from someone else’s work, ask yourself the following questions

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Analyze the data of the students in the statistics class problem

  1. The individuals are the __________
  2. Number of variables are ________
  3. Scores are __________
  4. Exam1, Exam2, Homework, Final, Project, Total Points all have _________ as the units
  5. There are no ________ for ID and grade
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eight
students
variables
nine
units
points
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Individual variables such as gender and height can be measured numerically

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Categorical and quantitative variables

  1. A _________ places an individual into one of two or more groups or categories.
  2. A _________ takes numerical values for which arithmetic operations such as adding and averaging make sense.
  3. The ________ of a variable tells us what values it takes and how often it takes these values.
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quantitative variable
categorical variable
distribution
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Variables for students in a statistics course

Suppose the data for the students in the introductory statistics class were also to be used to study relationships between student characteristics and success in the course. For this purpose, we might want to use a data set like the spreadsheet in Figure. Here, we have decided to focus on the TotalPoints and Grade as the
outcomes of interest. Other variables of interest have been included: Gender, PrevStat (whether or not the student has taken a statistics course previously),
and Year (student classification as first, second, third, or fourth year).

ID is a , total points is a , and the remaining variables are all categorical.

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categorical variable
quantitative variable
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It is possible to transform categorical variables into quantitative variables

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All quantitative variables are simple ones that could be counted

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A poor choice of variables can lead to misleading conclusions

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Accidents for passenger cars and motorcycles

The government’s Fatal Accident Reporting System says that 27,102 passenger cars were involved in fatal accidents in 2002. Only 3339 motorcycles had fatal accidents
that year. 

Does this mean that motorcycles are safer than cars? 

Note: the number of cars is by far higher than the number of motorcycles.

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Explanation

Exploratory data analysis basic strategies are

  • Begin by examining each variable by itself. Then move on to study the relationships among the variables.
  • Begin with a graph or graphs. Then add numerical summaries of specific aspects of the data
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sin cos tan
sin-1 cos-1 tan-1 π e
xy x3 x2 ex 10x
y√x 3√x √x ln log
( ) 1/x % n!
7 8 9 + MS
4 5 6 – M+
1 2 3 × M-
0 . EXP ÷ MR
± RND C = MC

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