Unit 4

Statistics 1-variable

Intro Problem• A farmer is investigating the effect of a new organic

fertilizer on his crops of peas. He has divided a small garden into two equal plots and planted many peas in each. Both plots have been treated the same except that fertilizer has been used on one and not the other.

• A random sample of 150 pods is harvested from each plot at the same time, the number of peas in each pod is counted.

• How many data samples did he collect?• What do you expect the data to look like?

Farmer’s Data

4 6 5 6 5 6 4 6 4 9 5 3 6 8 5 4 6 8 6 5 6 7 4 6 5 2 8 6 5 6 5 5 5 4 4 4 6 7 5 6

7 5 5 6 4 8 5 3 7 5 3 6 4 7 5 6 5 7 5 7 6 7 5 4 7 5 5 5 6 6 5 6 7 5 8 6 8 6 7 6

6 3 7 6 8 3 3 4 4 7 6 5 6 7 4 7 3 7 7 6 7 7 4 6 6 5 6 7 6 3 4 6 6 3 7 6 7 6 8 6

6 6 6 4 7 6 6 5 3 8 6 7 6 8 6 7 6 6 6 8 4 4 8 6 6 2 6 5 7 3

Without fertilizer

Without Fertilizer

6 7 7 4 9 5 5 5 8 9 8 9 7 7 5 8 7 6 6 7 9 7 7 7 8 9 3 7 4 8 5 # 8 6 7 6 7 5 6 8

7 9 4 4 9 6 8 5 8 7 7 4 7 8 10 6 10 7 7 7 9 7 7 8 6 8 6 8 7 4 8 6 8 7 3 8 7 6 9 7

6 9 7 6 8 3 9 5 7 6 8 7 9 7 8 4 8 7 7 7 6 6 8 6 3 8 5 8 7 6 7 4 9 6 6 6 8 4 7 8

9 7 7 4 7 5 7 4 7 6 4 6 7 7 6 7 8 7 6 6 7 8 6 7 10 5 13 4 7 11

Questions about farmer problem1) Can you state clearly the problem that the farmer wants to solve?2) How has the farmer tried to make a fair comparison3) How could the farmer make sure that his selection was at random4) What is the best way of organizing this data5) Are there any abnormally high or low results and how should they

be treated?6) How can we best describe the most typical pod size?7) How can we best describe the spread of possible pod sizes?

1) What does spread mean?8) Can the farmer make a reasonable conclusion from his

investigation?

Vocabulary• Population- a defined collection of individuals or objects about

which we want to draw conclusions• Census- The collection of information from the whole population• Sample- a subset of the population. It is important to choose a

sample at random to avoid bias in the results• Survey- the collection of information from a sample• Data (singular- datum) information about individuals in a

population• Parameter- a numerical quantity measuring some aspect of a

population• Statistic- a quantity calculated from data gathered from a sample.

It is usually used to estimate a population parameter

Why vocabulary is important in math…to understand Math jokes

Chapter 7 Part ATypes of Data

• Categorical Variables and Data• There is an 80% chance students are wearing

a blue polo to school– The data collected is ______ and ______– _______ is called a categorical variable because is

describes a particular quality or characteristic.– The collection of categorical variables is called

categorical data– Say categorical five times fast

• Quantitative or numerical variables- Discrete• the number of people in the lunch line– Is an example of a quantitative variable because it

has a numerical value. – The total number of people in the lunch line is

called numerical data – This is also an example of quantitative discrete

variable because the number of people in the lunch line is an exact number value that is often a result of counting• Basically that is a fancy way of saying there can’t be a

half a person. The informal definition is that --Discrete means we can count it.

• Quantitative or numerical variables- Continuous

• The times it takes to run a 100 m race – Quantitative variable because the answers are

numerical values– It is a quantitative CONTINUOUS variable because

it can take any numerical value within a certain range. It is usually the result of measuring.

Ready to classify these variables into• -categorical

quantitative discreteor quantitative continuous

a) The number of heads when 3 coins are tossedb) The brand of toothpaste used by the students in a classc) The heights of a group of 15 year old childrend) The number of years passed since you deposited $4,000 into a bank

account that earns 2% interest every yeare) The types of shoes students are wearingf) The grades you earn that show up on your transcriptg) Your ACT scoreh) The colleges that the graduating of class of 2013 go toi) The distance for your house to school

……now complete Exercise 7A

Chapter 7B- simple quantitative discrete data

• Frequency Table• the frequency of a data value is the number of

times that value occurs in the data set• Relative frequency- the frequency divided by

the total number of recorded values. It gives us the proportion of results

• Go back to the peas in a pod problem…

This is a frequency table: complete the table

Column Graph/Frequency Polygon• Range is on the ____________axis• The frequency of scores is on the ____ axis• The column widths are equal• There are gaps between columns to indicate the data is • How did I make the frequency polygon?

•

Make a Dot Plotname 3 characteristics about the dot

plot:

Will all data look so uniform as the peas in the pod?

Name 2 research questions that you could actually research and two that

you wouldn’t be able to research Quality research questions• • • •

Bogus questions• • • •

WHAT DO YOU THINK AN OUTLIER IS?

If you thought about penguins, you are correct

Who is the outlier?

Now let’s do an example….

Let’s do exercises 7B

• Complete 1a-g in class• Homework- problem 2 and 3• In class tomorrow review problems 2 and 3• Complete 4 and 5• Because Friday we have a quiz on this!