Common Core Math I Unit 1 OneVariable Statistics
Common Core Math I Unit 1: One-Variable Statistics Measures of Center and Spread
Describing Data Numerically • Measures of Center – mean, median • Measures of Spread – range, interquartile range, standard deviation S-ID. 2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets.
Think About the Situation Lets imagine stacked cubes representing each household from Group A. Use the stacks to answer the following questions. How could we rearrange to find the mean? Family 1 Family 3 Family 2 Family 5 Family 6 Family 4 Adapted from Data About Us, Connected Mathematics 2, Grade 6
Finding the Mean Make stacks all the same height by moving cubes. Family 1 Family 5 Family 3 Family 2 Family 4 Family 6 Adapted from Data About Us, Connected Mathematics 2, Grade 6
Finding the Mean • How many cubes are in each stack? • By leveling out the stacks to make them equal height, you have found the average, or mean, number of people in a household. What is the mean number of people per household? Ossie Gary Leon Paul Ruth Arlene Adapted from Data About Us , Connected Mathematics 2, Grade 6
Thinking About the Situation
Mean You can also think of mean as a balancing point, or making sure everyone has the same amount.
The Formula
Investigation 2: Using the Mean
Investigation 3: Using the Mean 1) Find the following: a) the total number of students b) the total number of movies watched c) the mean number of movies watched 2) A new value is added for Carlos, who was home last month with a broken leg. He watched 31 movies. a) How does the new value change the distribution on the histogram? b) Is this new value an outlier? Explain. c) What is the mean of the data now? d) Compare the mean from question 1 to the new mean. What do you notice? Explain. e) Does this mean accurately describe the data? Explain.
3) Data for eight more students is added. a) Add these values to the list in your calculator. How do these values change the distribution on the histogram? b) Are any of these new values outliers? c) What is the mean of the data now? Movies Watched 12 10 Frequency 8 6 4 2 0 0 5 10 15 20 25 Number of Movies 30 35 More
How do I know which measure of central tendency to use? http: //regentsprep. org/REgents/math/ALGEBRA/AD 2/measure. htm
Investigation 4: Mean vs. Median The heights of Washington High School’s basketball players are: 5 ft 9 in, 5 ft 4 in, 5 ft 7 in, 5 ft 6 in, 5 ft 5 in, 5 ft 3 in, and 5 ft 7 in. A student transfers to Washington High and joins the basketball team. Her height is 6 ft 10 in. Discuss and solve in your groups!
Mean vs. Median Mound-shaped and symmetrical (Normal) Skewed Left Skewed Right
Ticket out the Door What happens to the mean of a data set when you add one or more data values that are outliers? Explain. What happens to the mean of a data set when you add values that cluster near one end of the original data set? Explain why you think these changes might occur.
- Slides: 15