1. Warm-Up Take out a sheet of paper. Do NOT put your name on it. Answer the questions below on your paper. Be sure to number your responses. 1. What is your favorite color? 2. How many siblings do you have? 3. How many states (in the U.S.) have you visited? 4. How many times did you visit Bojangle’s in the past month? 5. How many times did you visit Buffalo Wild Wings in the past month? 6. Do you buy your lunch at school or do you bring it from home? (or neither) 7. If you could attend any college, which would it be? 8. How many pets do you have? 9. Do you have a checking/savings account?

2. Sampling Mean, Median, Mode Day 1

3. Population & Sample Population: collection of individuals or objects we want to know something about Ex: CHS students Census: Collecting data by going through every member of the population Survey (or poll): collecting data only from some members of the population Sample: smaller collection of the population which you will poll, survey or collect data on Ex: Mrs. Pleasant’s class Sampling: The act of selecting the sample

4. Basic Philosophy behind Sampling: We want a sample that is “representative” of the entire population Then, whatever we want to know about the entire population can be found by getting information from the sample Reliable data

5. Sampling Target population: distinguish the population fro which the survey applies Sampling frame: actual subset of the population which the sample will be drawn **Ideal when sampling frame is same as target population.***

6. Goal of Sampling ·To obtain results that accurately portray the population ·We want to be UNBIASED!!! A sampling method is called BIASED if it systematically favors some outcomes over others. A sample is biased if certain members are underrepresented or overrepresented, SELECTION BIAS. Nonresponse Bias: response rate for survey low ·Sampling bias means that the data you collect may not be accurate or represent the group. Bias can make your data unreliable.

7. Why does bias matter? Ex: A company wants to survey local residents about their dry cleaning usage. They use a sample picked from a list of telephone numbers of people living in a particular county. Why is this sample biased? Who could be missed? Ex: a survey of high school students to measure teenage use of illegal drugs. Why is this sample biased? Who is missed?

8. Types of Sampling Simple Random Sampling · Each person has equal probability of being picked to participate as any other person in population Ex: Draw names from a hat Ex: Lottery – each number has same probability of being drawn as the other numbers C luster Sampling · Only poll a certain group Ex: if we want to know something about the whole student body, but only sample seniors

9. Types of Sampling, cont’d Convenience Sampling · Poll a group of individuals who are readily available (Short cut to sampling) Data should be scrutinized and could be too unreliable. ·Ex: poll your friends or classmates S ystematic Sampling: individuals are arranged in some sort of order and then selected ·EX: Polling every 10 th person on a SIMS list

10. Types of Sampling, cont’d Stratified Sampling Breaking the sampling population into categories (Strata) then randomly choosing a sample from these strata. · Strata: a group within a population that shares a common characteristic Substrata: strata sub divided further · Ex: Freshmen/Sophomore/Junior/Senior (breaking CHS population into stratas) Breaking each call down into male/female (Substratas) Sampling randomly selected senior males, senior females, junior males, etc.

11. Types of Sampling, cont’d Quota Sampling: Systematic effort to force the sample population to be representative of the given population through use of quotas. EX: Sample surveyed should have so many women, men, black/white/hispanic people, employed/unemployed, etc… Proportions of each should be the same as the population Produce reliable data

12. Mean, Median, and Mode ·Mean: average (all up all the numbers in data set and divide by # of terms) ·Median: place data in ascending order (least to greatest OR greatest to least), pick the middle number ·Mode: number which appears MOst often

13. Example 1: Average weekend temperatures in NC for July 879210099 94949294 Find the mean, median, mode. Median = 94 Mode = 94

14. You Try!!! Find the mean, median and mode for the follow set of data: 8378817780807982 Mean = 80 Mode = 80 Median = 80

15. Standard Deviation The measure of how each value in the data varies from the mean. The average distance from the mean Steps to finding the Standard Deviation: 1)Find the mean of the data set 2)Subtract the mean from each of the numbers in the data set 3)Square each difference from step 2 4)Find the mean of the square numbers 5)Take the square root of the new mean to find standard deviation.

16. Example 1: Standard Deviation Find the standard deviation for the following values: 50, 60, 70, 80, 80, 90, 100, 110 Step 1 – Find the mean of the data Mean = 80 Step 2 – Subtract the mean from each of the #’s in the data set -30, -20, -10, 0, 0, 10, 20, 30 Step 3 – Square each of the values from step 2 900, 400, 100, 0, 0, 100, 400, 900 Step 4 – Find the mean of new data set Mean = 350 Step 5 – Take square root of mean in step 4 to find Standard deviation SD = about 18.71

17. Example 2: Standard Deviation Find the standard deviation for the following values: 78.2, 90.5, 98.1, 93.7, 94.5 Step 1 – Find the mean of the data Mean = 91 Step 2 – Subtract the mean from each of the #’s in the data set -12.8, -0.5, 7.1, 2.7, 3.5 Step 3 – Square each of the values from step 2 163.84, 0.25,50.41, 7.29, 12.25 Step 4 – Find the mean of new data set Mean = 46.808 Step 5 – Take square root of mean in step 4 to find Standard deviation SD = about 6.842

18. You Try!!!: Average weekend temperature in NC for July 879210099 94949294 Find the standard deviation. Step 1: Mean = 94 Step 2: -7, -2, 6, 5, 0, 0, -2, 0 Step 3: 49, 4, 36, 25, 0, 0, 4, 0 Step 4: Mean = 14.6 Step 5: SD = about 3.84