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Learn about the difference between random and biased samples in data collection, and how they can affect the results obtained. Explore case studies and practice problems to enhance your understanding.
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Random or Biased Sample? • Nina wants to know how the students in her school feel about the new dress code. She randomly selects the names of 100 students from a school list and e-mails each of them a survey. She waits for responses and records data from surveys that are returned to her. Consider: • How did Nina choose the students whom she e-mailed the survey? • What data did she receive and record? Nina did not receive surveys back from every student she e-mailed, so this is BIASED. This is known as voluntary response bias. The students who took the time to fill out the survey are more likely to feel strongly about the dress code, and those who feel less strongly may not have bothered to return it.
Random or Biased? • Trey wants to know how the students in his school feel about the new dress code. He surveys all the students in his homeroom. Consider: • How did he choose the students surveyed? • What data did he receive and record? Not every student in Trey’s school had a chance of being selected, so this is a BIASED SAMPLE. This is an example of a convenience sample that was probably chosen because it was easy for him to survey them. This sample is not representative of his entire school.
Make predictions from a random sample • Sarah randomly surveyed 80 students at her school. She found that 15 out of the 80 students she surveyed chose pizza as their favorite school lunch option. If there are 700 students at her school, predict how many students at her school would choose pizza as their favorite lunch option. 1. Set up a proportion: = 2. Multiply the numbers across from each other, then divide by the third number: 15(700) ÷ 80 = 131.25 3. Is your answer reasonable? Do you need to round your final answer?
Find the mean of a set of data • Mean = • Anja wants to know the mean age, in months, of seventh – grade students at her school. She chooses 20 seventh - grade students at random to survey and records their ages, in months. Her data are below: 156 160 150 162 158 150 158 156 155 168 154 153 157 160 161 152 145 148 153 154 Estimate the mean age, in months, of a 7th grade student at her school. Mean = = 155.5 ≈156 months Since this is a random sample, it is most likely representative of the population (all 7th graders at her school).
Creating a Dot & Box Plot • Dot plot: • Find the range (highest & lowest values) of your data set. • Draw and label a number line to include all values in the data set. • Place one dot above the number in the number line for each time the value is recorded in the data set. If the number 5 is listed 3 times, then there should be 3 dots above the number 5. • Box Plot: how to make a box plot
Dot & Box plots 3. What are the most common ages of children that use the library? 4. The range of ages of children that use the library is from _____ to _____. 5. What is the median age of children that use the library? 4 & 7 4 11 6.5
Practice: • Complete the front of the handout (p. 148 -149). • Check your answers. See me if you have questions. • Complete my.hrw.com lesson 10.2. You are only allowed to skip the orange dot. Remember this is for a quiz grade! Done? Here are your options: Correct or retake a test. Do previously assigned lessons on my.hrw.com or khanacademy.org. Prodigy, only if all assignments are turned in and you are passing.
