1.2 KEY TERMS• Statistics:The collection, analysis, interpretation and presentation of data

• Population: A collection of persons, things or objects under study (ex. All students at FBHS)

• Sample: A portion or subset of the larger population to collect data from and study (ex. This class as a subset of students at FBHS)

• Statistic: A number that represents a property of the sample (ex. If this class is a sample of the school, the average GPA of this class)

• Parameter: A number that is a property of the population (ex. The average GPA of all FBHS students)

• Variable: (X or Y) a characteristic of interest for each person or thing in a population

• Numerical variables: Take on values with number measures (ex. Weight in lbs., time in min.)

• Categorical variables: Place the person or thing in a category (ex. If X is favorite colors, examples could be purple, blue, etc.)

• Data: values for the variable from each individual

IDENTIFY THE POPULATION, SAMPLE, PARAMETER, STATISTIC, VARIABLE AND DATA:

To determine the average time FBHS students take to get ready in the morning, we ask each student in one English class how long they take.

Population = all FBHS students

Sample = students in the English class

Parameter = average time for all students

Statistic = average time for the English class

Variable = X = time it takes one student

Data = ex. 20 min., 1 hour, 35 min.

IDENTIFY THE POPULATION, SAMPLE, PARAMETER, STATISTIC, VARIABLE AND DATA:

A phone survey is conducted to determine what proportion of eligible voters have already decided for whom they will vote for president

Population = all eligible voters

Sample = voters called

Parameter = proportion of voters already decided

Statistic = proportion of called voters already decided

Variable = Y = the number of voters who have already decided

Data = decided, undecided

PRACTICE: IDENTIFY THE POPULATION, SAMPLE, PARAMETER, STATISTIC, VARIABLE AND DATA:

To determine how long, on average, U.S. high school students sleep a night, all students from 10 randomly selected schools are asked

Population = U.S. high school students

Sample = students in the 10 chosen schools

Parameter = average time sleeping of U.S. students

Statistic = average time sleeping of students in the 10 chosen schools

Variable = X = time one student sleeps

Data = hours, ex. 7 hours, 5 hours, 9 hours

1.3 KEY TERMS

• Qualitative data: categorize or describe a population (ex. Hair color, favorite music, blood type)

• Quantitative data: Always numbers (ex. Height, number of people with a certain trait)

• Quantitative discrete: data that can take on only certain numerical values (ex. Number of days per week someone exercises, number of magazines a person reads)

• Quantitative continuous: data that results from measuring (ex. Time spent in line, weight of fruit)

WORK COLLABORATIVELY TO DETERMINE THE CORRECT DATA TYPE (QUANTITATIVE OR QUALITATIVE). INDICATE WHETHER QUANTITATIVE

DATA ARE CONTINUOUS OR DISCRETE. HINT: DATA THAT ARE DISCRETE OFTEN START WITH THE WORDS "THE NUMBER OF."

a. the number of pairs of shoes you own

b. the type of car you drive

c. where you go on vacation

d. the distance it is from your home to the nearest grocery store

e. the number of classes you take per school year.

f. the tuition for your classes

g. the type of calculator you use

h. movie ratings

i. political party preferences

j. weights of sumo wrestlers

k. amount of money (in dollars) won playing poker

FIGURE 1.3

What type of data does this pie chart display?

FIGURE 1.4

What type of data does the graph display?

FIGURE 1.5

Pie chart to display qualitative data.

FIGURE 1.6

This bar graph displays the same data as the previous chart.

FIGURE 1.7

What do you notice about this bar graph?

FIGURE 1.8

What do you notice about this bar graph?

FIGURE 1.9

Bar graph with Other/Unknown Category

FIGURE 1.10

Pareto Chart With Bars Sorted by Size

FIGURE 1.11

Organization matters!

1.2 KEY TERMS (CONT.)

• Random sampling: each member of a population has an equal chance of being selected for the sample. The goal is that the sample has the same characteristics of the population

• Simple random sample: choose n objects at random (ex. Put numbers in a hat, use a random number generator)

• Stratified sample: divide the population into groups (strata) and choose an equal proportion from each stratum

• Cluster sample: divide the population into groups (clusters) and randomly select some of the clusters

• Systematic sample: randomly select a starting point and take every nth piece of data from a listing of the population

• Convenience sample: using results that are readily available• Sampling bias: when a sample is collected and some

members of the population chosen are not as likely to be chosen as the others

FIGURE 1.12

VARIATION HAPPENS!• Samples WILL be different, even on well chosen samples. We try to choose

representative samples to get as close as we can to the parameter, but any statistic WILL have variability

• There are some critical errors to be looking for:

• Problems with samples: a non-representative sample• Self-selected samples: responses by people who choose to respond• Sample size issues: large samples are better• Undue influence: collecting data or asking questions in a way that

influences the response• Non-response or refusal of subject to participate: The collected

responses may no longer be representative of the population.• Causality: A relationship between two variables does not mean that one

causes the other to occur• Self-funded or self-interest studies: A study performed by a person or

organization in order to support their claim.• Misleading use of data: improperly displayed graphs, incomplete data,

or lack of context• Confounding: When the effects of multiple factors on a response cannot

be separate

FIGURE 1.14

As the graphs show, Acme consistently outperforms the Other Guys!

Examining this statement, as a statistician, what do you notice?

FIGURE 1.15

What critical errors do you notice with this graph?

1.4 KEY TERMS• Frequency: The number of times a value of data occurs

• Relative Frequency: the ratio (fraction or proportion) of the number of times a value of the data occurs in the set of all outcomes to the total number of outcomes

• Cumulative relative frequency : the accumulation of the previous relative frequencies.

CREATE A FREQUENCY TABLE FOR HOW LONG EVERYONE SLEPT LAST NIGHT

Hours Tally Frequency Relative Frequency

Cumulative Relative Frequency

3

4

5

6

7

8

9

• What percent of people slept 8 hours?

• What percent of people slept up to 7 hours?

• What percent of people slept at least 6 hours?

FIGURE 1.13

Which graph represents cumulative relative frequency?