Data Analysis Unit 8 Day 3

Measures of Center There are two ways to find the center of Mean – the value that locates the balance point / center of the data collected. This also is known as the average! Note: mean uses every data value How do you calculate it? 𝒂𝒅𝒅 𝒂𝒍𝒍 𝒐𝒇 𝒕𝒉𝒆 𝒅𝒂𝒕𝒂 𝒗𝒂𝒍𝒖𝒆𝒔 𝒏𝒖𝒎𝒃𝒆𝒓 𝒐𝒇 𝒅𝒂𝒕𝒂 𝒗𝒂𝒍𝒖𝒆𝒔 Median – the value that divides the data in half. Note: the data must be in order! How do you calculate it? Write the data in order, then find the middle value

Which measure of center should we use? The mean is used when there are no outliers in the collected data. The median is used when there are outliers in the collected data.

Example Version 1 Version 2 92, 98, 89, 94, 90 92, 98, 89, 94, 53 92, 98, 89, 94, 90 92, 98, 89, 94, 53 Mean: 92.6 Mean: 85.2 Median: 92 Median: 92    How do the mean and median values compare in Version 1? Version 2? Version 1 – the mean and median values are high and are different by 0.6 Version 2 – the mean and median values are high and are different by 9.8 How did the outlier affect the mean in Version 1? Version 2? Version 1 – the outlier did not affect the mean Version 2 – the outlier dropped the mean value   Note!... If the mean and medians value are similar, then there is no outlier If the mean and median values are different, then there is an outlier  

Measures of Spread Spread – is how far apart the data values are. There are three ways to find the spread of the data: Range How do you calculate it? highest value - smallest value Standard Deviation Note: used when the mean is a better option for spread How do you calculate it? Calculated by a complex formula, so we’ll use the calculator for assistants!   Interquartile Range Note: used when the median is a better option for spread How do you calculate it? Q3 – Q1 (find on the calculator)

Student Height Scenario Example Three students at Lake Norman High School were instructed to collect data on student heights for males in their school. Each were allowed to approach the study in their own way.

Alex’s Study Alex decided to visit each classroom during 3rd block and asked two random males in front of the class to state their height. Alex then recorded all of the data below: Height of Males at our School in inches 63, 71, 64, 67, 68, 69, 85, 71, 64, 66, 65, 68, 67, 72, 69, 68, 69, 68, 70, 73 Range: Mean: Median: Standard Deviation: Interquartile Range:

Bella’s Study Bella decided to make a list of all male students. She randomly chose the 15th student on the list and then chose every 7th male afterward until she had 20 males. When meeting with each, she asked them: “Most males have a height of at least 68 inches, so what is your height? Bella then recorded the responses below: Height of Males at our School in inches 69, 67, 71, 68, 68, 70, 66, 62, 75, 70, 65, 67, 69, 68, 68, 66, 68, 68, 73, 62 Range: Mean: Median: Standard Deviation: Interquartile Range:

Caleb’s Study Caleb plays on the basketball team so he decided to use his teammates for his data. He measured each of their heights with a tape measure and recorded the data below. Height of Males at our School in inches 71, 75, 76, 78, 74, 72, 75, 68, 71, 69, 76, 83, 66, 70, 71, 73, 62, 64, 71, 68 Range: Mean: Median: Standard Deviation: Interquartile Range:

Follow-Up Questions 1. What type of sampling method did each student use? Alex Bella Caleb Stratified Systematic Convenience 2. If possible, how could Alex’s data be bias? None – he used stratified sampling method 3. How do you think Alex’s bias influenced the data? It’s not influenced, because Alex’s collected his data in a non-bias way.

Follow-Up Questions 4. If possible, how could Bella’s data be bias? Leading questions   5. How do you think Bella’s bias influenced the data? The males will say that they are taller than what they are 6. If possible, how could Caleb’s data be bias?   Convenience – only asked basketball player who are commonly taller 7. How do you think Caleb’s bias influenced the data? He got really tall people for his data

Follow-Up Questions 8. Which student’s data reflects an overall taller male populace? Explain your answer Caleb. When comparing the means and medians from all three study, Caleb’s data was always higher. 9. Which student’s data overall reflects the least spread out data? The most spread out data? Explain your answer Belle, because her range was the smallest. Alex, because his range was the largest. 10. Which student most likely has an outlier in the data? Explain your answer. Alex. His mean and median are the furthest apart. Also, most of his data was in the 60’s and 70’s and had one person who was 85 inches tall.