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Statistics

Unit 1

Data and Displays

6 topics · 24 practice questions · Free responseNot yet reviewed

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Notes

Types of data

  • An individual is one person or thing in a data set. A variable is a characteristic measured on each individual.
  • Categorical variables put individuals in groups. Quantitative variables are numbers that can be averaged, either discrete (counts) or continuous (measurements).
  • Numbers used as labels, like zip codes, are categorical.

Displays for categorical data

  • Bar graphs show counts or percents with separated bars. Pie charts show parts of a whole that add to $100\%$; the central angle is percent $\times\ 360^\circ$.
  • Relative frequency $\displaystyle = \frac{\text{count}}{\text{total}}$.

Displays for quantitative data

  • Dot plots and stem plots show every value. Histograms group values into equal-width bins with touching bars.
  • Describe a distribution by its shape (symmetric, skewed right, skewed left, unimodal, bimodal, uniform), center, spread and unusual features. The skew is named for the tail.

Topics in this unit

Each topic has its own short notes and practice.

Practice

Which of these variables is quantitative?
In a class of 25 students, 7 are left-handed. The relative frequency of left-handed students is:
A stem plot has rows $0 \mid 5\ 8$, $1 \mid 2\ 6\ 6\ 9$ and $2 \mid 3$ with key $1 \mid 6 = 16$. How many values are from 10 to 19?
A histogram of the number of minutes students spend on social media has most values low and a long tail toward large values. The shape is:
In a pie chart, a category makes up $20\%$ of the data. Its central angle is:
Which data set should be shown with a histogram rather than a bar graph?

Free response

Write your answer first, then open the scoring guide.

Free-response question

A survey of 20 students asked about their pets. The results: 8 have a dog, 6 have a cat, 2 have a fish and 4 have no pet.

(a) Find the relative frequency of each answer and show that they add to 1.

Show the answer and scoring guide

Dog $\displaystyle \frac{8}{20} = 0.40$, cat $\displaystyle \frac{6}{20} = 0.30$, fish $\displaystyle \frac{2}{20} = 0.10$, no pet $\displaystyle \frac{4}{20} = 0.20$. Sum: $0.40 + 0.30 + 0.10 + 0.20 = 1$.

Check off the points you earned:

(b) If the data are shown in a pie chart, what central angle should the dog slice have?

Show the answer and scoring guide

$0.40 \times 360^\circ = 144^\circ$.

Check off the points you earned:

(c) Is the type of pet a categorical or quantitative variable? Explain why a histogram would not be an appropriate display.

Show the answer and scoring guide

Categorical, because each student is placed in a category (dog, cat, fish, none). A histogram uses bins on a number line for a quantitative variable, so a bar graph or pie chart is appropriate instead.

Check off the points you earned: