Data Analysis Student Text :Chapter 7

Data Analysis 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 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 EQ: What is a sample? What is a subjective sample? What is a random sample? Today you will begin to learn about data analysis as we learn about different types of samples, and how they will influence data analysis!!!

Data Analysis Activation: Describe how you could find the average height of students in this class. How would you find the average height of boys/girls in this class? In this school? In this county? In this state?

Data Analysis Key Terms : Unit 4- Student Text Chapter 7 Population-a group of individuals, items, or cases with something in common that someone may want to study. Ex: High School Students, Teenagers, Educators, etc. Sample-a subset of a population used to make predictions about the larger population Ex: Howard High School Students, Bibb County Teenagers, Bibb County Educators, etc. – subjective sample is a sample that is chosen based on some criteria; a subjective sample is a sample that you think “best” represents the data set. – random sample is a sample that is produced by randomly selecting data; a random sample is a sample that may not represent the data set the “best”.

Data Analysis unbiased sample- every member of the population has an EQUAL chance of being part of the sample; the chance of any member being included in the sample is random. Representative of the WHOLE population. biased sample- some members of the population are more likely to be included in the sample than others; members have an UNEQUAL chance of being included because the sample is not random. Not representative e of the WHOLE population.

Data Analysis ***Remember when sampling a population, it is important that the sample should be representative of the WHOLE population!!!*** FACT: In order for a sample to be representative of a whole population!! – an unbiased sample must be large enough to show all the variation within the population – a sample that is too small is not likely to be representative

Data Analysis MEAN- to calculate the mean (average) of a data set add together all the elements of the data set. Once you have the sum for the data set divide the sum by the total numbers of elements in the data set to obtain the mean. Examples:

Data Analysis MEDIAN -to find the median (middle term) of a data set arrange the elements in numerical order. If the data set includes an ODD number of terms the term that is exactly in the middle of the set is considered the median. If the data set includes an EVEN number of terms divide the two terms in the middle by two. The average value that you obtain from those two terms is the median. Examples:

Data Analysis MODE- This is the term or terms in a data set that occurs the most. A mode can be described as unimodal, bimodal, trimodal, etc. A data set can have more than one mode. Examples:

Data Analysis RANGE- To find the range of a data set place the terms of the data set in numerical order. Next, subtract the smallest term from the largest term. Example:

Data Analysis QUARTILE- – First (Lower) Quartile – Inter (Middle) Quartile – Third (Upper) Quartile

Data Analysis VARIANCE- the value that is the average squared distance between the mean and each data point of the data set.

Data Analysis STANDARD DEVIATION-this is the value that represents the square root of the variance Examples:

Data Analysis Review how to create a box-and-whisker plot

Data Analysis Summary Random Sample A random sample is more representative because there is no bias in selection, making it more probable that accurate information will be produced. Subjective Sample Subjective sample sets do not provide information which is as accurate as random samples.

Data Analysis Summary IMPORTANT FACT: The mean, variance, and standard deviation of a random sample can fairly accurately characterize the whole population!!!!!!!!!!!

Data Analysis Homework: Students Assignment pg Question 1-7

Data Analysis Activation: Describe how you could find the average height of students in this class. How would you find the average height of boys/girls in this class? In this school? In this county? In this state? Instruction: Notes on random and subjective samples, mean, and variance. Work: Complete examples of how to find mean, variance, and how to determine if random or subjective samples are better Assessment: Unit 4 Test TOTD: Write the difference between random and subjective samples