Data Analysis: Part 3 Lesson 7.1. Data Analysis: Part 3 MM2D1. Using sample data, students will make informal inferences about population means and standard.

Data Analysis: Part 3

Lesson 7.1


• MM2D1. Using sample data, students will make informal inferences about population means and standard deviations.

• a. Pose a question and collect sample data from at least two different populations.

• b. Understand and calculate the means and standard deviations of sets of data.

• c. Use means and standard deviations to compare data sets.


• d. Compare the means and standard deviations of random samples with the corresponding population parameters, including those population parameters for normal distributions.

• Observe that the different sample means vary from one sample to the next.

• Observe that the distribution of the sample means has less variability than the population distribution.


Activation:Calculate the median, mean, mode, and range the following data set. Create and Box and Whisker Plot. Find the Standard Deviation.Data Set: 8, 15, 10, 8, 16, 16, 10, 14, 9, 14

Homework/Answers


EQ: How does sampling affect the sample distribution?

Today you will begin to learn about data analysis as we learn about different sampling techniques!!


Fact: The values included in the box portion of the box and whisker plot (Q2) represents 50% of the data set; both the lower quadrant (Q1)

and upper quadrant (Q3) represents 25% of the data set


• Fact: If you have an even number of values, the first median was the average of the two middle values, then you include the middle values in your sub-median computations. If you have an odd number of values, the first median was an actual data point, then you do not include that value in your sub-median computations.

• Fact: The upper extreme is the upper range value and the lower extreme is the lower range value



Calculating Standard DeviationStep 1: Calculate the average for the ENTIRE data set

Step 2: Take each number (data point) and subtract the average from it

Step 3: Square each of the differencesStep 4: Add up all of the results from Step 3

Step 5: Divide the sum of the squares by the number of numbers in the data set minus one (N-1)

This gives you the VARIANCE of the data setStep 6: Take the square root of the number you get

This gives you the STANDARD DEVIATION of the data set


Unit Vocabulary Quiz (1/23 (B) & 1/24 (A)Know the following terms:

Mean Random SamplesRandom Number GeneratorStratified Random SamplingCluster SamplingVariance


Standard DeviationMedianModeRangeBiasSubjective Samples

***You must know the definitions as well as tell how to apply an example of the types of samples if

given an description***


Subjective vs. Random Sample Problem # 1 pg. 305 (1-7) in Student Text; Refer to pg. 311 for data information & p.308 (11-15)

Problem #2 pg. 309


Select five random number from the interval [ 1, 100]. Calculate mean, median, and range. List mode if there is one.***Use a Random Sample Table or Calculator in order to find random numbers***


Subjective vs. Random Sampling FactsFact: Random sampling results in a smaller range and interquartile range than subjective sampling.Fact: Random sampling is better because subjective decisions may produce nonrepresentative results


Homework:TOTD

Review Notes and Unit DefinitionsRemember do not just learn the definition, but

also how to apply them!!!!!!!!!!!!!


Stratified Random Sample- a random sample where the population is divided into two or

more groups according to some criteria (called strata) such as grade level or geographical

locationRefer to page 317, Problem #1


Clustered Sample- a random sample where the population is divided into clusters based on some criteria such as homerooms, family members, or geographical locations. A clustered sample is especially helpful when the size of the clusters is UNKNOWN.

(Refer to pg. 319 , Problem #2)


Example for Stratified Random SampleRefer to Problem #1 pg. 317 & Male Height chart on pg. 311 in Student Text


Homework: Pg. 139-141 (1-2)


Examples of Types of SamplesRandom Sampling : Ex. Choosing 100 fans at

random to participate in a survey from a crowd of 5000 people

Stratified Random Sample: Ex. If students in a high school are divided by class, and random

samples are then taken from each class ( freshman, sophomores, etc.)


Examples of Types of SamplesSubjective Sample: Ex. From a set of students “choosing five students you know” instead of

choosing students at random Clustered Sample: Ex. Students in a high school

class are divided into clusters of 20 students based on their student ID numbers. Each

group of 20 students is a clustered sample.


Activation: Calculate the median, mean, mode, and range the following data set. Create and Box and Whisker Plot. Find the Standard Deviation.Data Set: 8, 15, 10, 8, 16, 16, 10, 14, 9, 14Instruction: Notes on Subjective and Random SamplesWork: Complete Problem 1 & 2 (Lesson 7.1) in Student TextAssessment : MidUnit TestSummary: Describe the difference in your data using a subjective vs. a random sample.

Data Analysis: Part 3 Lesson 7.1. Data Analysis: Part 3 MM2D1. Using sample data, students will make informal inferences about population means and standard.

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