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 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.

Data Analysis: Part 3 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.

Data Analysis: Part 3 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

Data Analysis: Part 3 EQ: How does sampling affect the sample distribution? Today you will begin to learn about data analysis as we learn about different sampling techniques!!

Data Analysis: Part 3 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

Data Analysis: Part 3 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

Data Analysis: Part 3

Calculating Standard Deviation Step 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 differences Step 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 set Step 6: Take the square root of the number you get This gives you the STANDARD DEVIATION of the data set

Data Analysis: Part 3 Unit Vocabulary Quiz (1/23 (B) & 1/24 (A) Know the following terms: Mean Random Samples Random Number Generator Stratified Random Sampling Cluster Sampling Variance

Data Analysis: Part 3 Standard Deviation Median Mode Range Bias Subjective Samples ***You must know the definitions as well as tell how to apply an example of the types of samples if given an description***

Data Analysis: Part 3 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

Data Analysis: Part 3 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***

Data Analysis: Part 3 Subjective vs. Random Sampling Facts Fact: 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

Data Analysis: Part 3 Homework: TOTD Review Notes and Unit Definitions Remember do not just learn the definition, but also how to apply them!!!!!!!!!!!!!

Data Analysis: Part 3 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 location Refer to page 317, Problem #1

Data Analysis: Part 3 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)

Data Analysis: Part 3 Example for Stratified Random Sample Refer to Problem #1 pg. 317 & Male Height chart on pg. 311 in Student Text

Data Analysis: Part 3 Homework: Pg (1-2)

Data Analysis: Part 3 Examples of Types of Samples Random 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.)

Data Analysis: Part 3 Examples of Types of Samples Subjective 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.

Data Analysis: Part 3 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 Instruction: Notes on Subjective and Random Samples Work: Complete Problem 1 & 2 (Lesson 7.1) in Student Text Assessment : MidUnit Test Summary: Describe the difference in your data using a subjective vs. a random sample.