aim: what is statistics and why do we care?

Aim: Intro to Statistics Course: Alg. 2 & Trig.

Do Now: What is statistics and why do we care?

Aim: What is statistics and why do we care?


Statistics

is the science of collecting, organizing, analyzing, and presenting numerical data.

Situations where a statistical study would be useful

• A utility company wants to find how much money is spent by a typical American family to heats its home.

• The US Government wants to know how many people reside in the United States• The State Regents want to know how well students are performing the new math standards.


Statistics: Experimental vs. Observational

Experimental: a variable(s) of interest isidentified. Then other variables are identified and controlled so data can be obtained about how they influence the variable of interest.

Example: Pharmaceutical company might be interested in how a new drug affected blood pressure. It controls dosage, age, etc.

Observational: no attempt to control any variables.

Example: Survey to determine consumer opinions – written responses; or strictly observational – counting the number of times an event occurs.


Sample

SamplingSampling

The Stay-Brite Light Bulb Company makes millions of light bulbs. How can the Stay-Brite Light Bulb Company determine the average life of its light bulbs?

A study based on surveying a portion or sample of a population - results reflect that of entire population.

• Must be fair and reflect entire population

• Must be fair and reflect entire population

• Must contain a reasonable number of items being tested or counted

• Must contain a reasonable number of items being tested or counted

• Selection must be random• Selection must be random


Sampling

To determine which television programs are the most popular in a large city, a poll is conducted by selecting people at random at a street corner and interviewing them. Outside of which location would the interviewer be most likely to find a fair sample? 1) a ball park 2) a concert hall

3) a supermarket Explain

The student government wishes to interview a sample of students to determine the general interests of the student body. Two questions are to be asked, “Do you want more pep rallies?” and “Do you want more dances?” What location in the school would result in a fair sample? Explain


Model Problem

Suppose you were one of the students in charge of planning the senior trip. The choices are a baseball fantasy camp, Colonial Williamsburg, or Disney World. For each of these choices, explain how you would design a study that would be BIASED so that it would lead people to believe that most seniors want to go to that particular trip.


Model Problem

A group of 8 students decided that they wanted to lose weight. Four of them decided to walk a mile each school day before school. The other four of them decided to walk a mile each day after school. All weigh themselves each Wednesday and report their weight to their math teacher, who is keeping it confidential. One student says this is an experiment. A 2nd disagrees and says its an observational study. A 3rd thinks it’s a survey. Explain which it is.


Data Collection & Organization

How many members in your immediate family (living in same household)?

Organizing Data:Organizing Data:

Frequency Table-

Tally Frequency


Organizing Data

Frequency Table-

Tally Frequency

Grouped (Intervals) DataGrouped (Intervals) Data

A teacher marked a set of 32 papers. The grades were as follows: 90, 85, 74, 86, 65, 62, 100, 95, 77, 82, 50, 83, 77, 93, 72, 98, 66, 45, 56, 100, 50, 89, 78, 70, 75, 95, 80, 78, 83, 81, 72, 75.


Organizing Data

Intervals - The rules for grouping dataIntervals - The rules for grouping data

• The intervals must cover the complete range of values. The range is the difference between the highest and lowest values.

•The intervals must be of equal size.

•The number of intervals should be between 5 and 15.

•There must not be overlapping intervals and every count/tally must fall into one and only one interval.


Organizing Data

Frequency Table-

Tally Frequency

In order to determine how many people use a school cafeteria daily, a count is made for a month. The following numbers were obtained:

1st wk: 221, 242, 280, 252, 261; 2d wk: 229, 233, 277, 246, 269; 3rd wk: 236, 251, 281, 241, 254; 4th wk: 227, 246, 272, 246, 249. Construct an interval frequency table for data.

What is the

range?


Regents Question

Which task is not a component of an observational study?(1) The researcher decides who will make up the sample.(2) The researcher analyzes the data received from the sample.(3) The researcher gathers data from the sample, using surveys or taking measurements.(4) The researcher divides the sample into two groups, with one group acting as a control group.


Regents Question

Howard collected fish eggs from a pond behind his house so he could determine whether sunlight had an effect on how many of the eggs hatched. After he collected the eggs, he divided them into two tanks. He put both tanks outside near the pond, and he covered one of the tanks with a box toblock out all sunlight. State whether Howard’s investigation was an example of a controlled experiment, an observation,or a survey. Justify your response.

aim: what is statistics and why do we care?

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