Samples and Populations Making Comparisons and Predictions

Making Sense of Samples Investigation 1 Making Sense of Samples

Homework Pg 20 due 4/26 A 1, 3, 4,8,14, 15,16,27,28 B 2, 3,4,14,15,16,33 IXL K5 and K8 write and solve proportions due 4/26

Vocab – most we already discussed and defined Mean Median MAD Line Plot Numerical Data Categorical Data Interquartile Range (IQR) Box and Whisker plot Relative Frequency frequencies based on percentages Census official count or survey of a population Population entire collect of data

Invest 1.1 Comparing Performances Using Center and Spread Given a set of results, how might you use measures of center and variability (spread) to judge overall performance?

Notes Be able to calculate the mean, median, and MAD Be able to compare the data from these measures

Example pg 8 Find the mean and median of Jun’s and Mia’s scores. What do you notice? both are 80 for both students 2. Compare Jun’s and Mia’s test performances can’t tell from data Determine the range and MAD of Jun’s test scores 40 and 13.33 Determine the range and MAD of Mia’s test scores 10 and 3.33 5. Compare this data

6. Do you have enough data to make any general statements about Jun’s or Mia’s overall math test performance? Explain not a large enough data set Decide whether you agree or disagree with each statement below. Use the statistics you have found so far to help explain your reasoning. One student is a stronger math student than the other One student is more consistent than the other The two students perform equally well on math tests You can make better comparisons using a larger data set

Homework You should be able to complete 1 and 2

Invest 1.2 Which Team is Most Successful Using the MAD to Compare Samples What strategies might you use to evaluate numerical outcomes and judge success?

Notes Be able to make a line plot of the data Use a number line Mark x’s above numbers that are represented in the data Determine which comparisons can be make accurately base on the graphs and data

Example pg 10 Use page 10 to answer problem 1.2 Make a line plot for each teams data: what comparisons can you make Look at the 3 strategies listed on page 11 Explain whether or not the strategy helps determine the most successful team 1. total raised is the same, so doesn’t help determine most successful 2. since totals are the same aver will be the same except for team 5, less members, teams 5 will be higher because of same amount with less people which could mean more successful 3. MAD is closer with team 6, means more consistent among the team, if using variability want the lowest possible to help determine most successful

Problem 1.2 Lets look at D 2 about 33% 6 100% 0 data points more than 2 MAD’s Data located within 2 MAD’s is almost always 100%

Homework You should be able to complete 3-7 More notes you could add Line plot is a visual for range, min and max values help with spread Each piece of statistics could be used but depends on how you want to interpret the data MAD is average distance from mean Majority of data is within 2 MADs of mean

Invest 1.3 Pick Your Preference Distinguishing Categorical Data from Numerical Data How might you compare results to see if each sample responds to a survey in a similar way? How can using percentages help you make comparisons?

Notes Remember how to make a bar graph categories on the bottom frequency on the side Know what categorical data is things such as favorite color Calculate a percent from a fractions divide fraction and multiple by 100 denominator is how many took survey

Example pg 13 Calculate the relative frequency for each table Make a bar graph, all can be on the same graph This is called a double bar graph Preference is the x-axis and relative frequency is the y-axis Which measures M,M, M can you use to describe the results Mode because it is categorical Suppose 400 people ride a roller Coaster in one day. How many would you predict want to sit up front? About 200

Homework You should be able to complete 8, 27-31 Look at the x-axis if there are words here it is categorical Making a relative frequency table to use on a bar graph

Invest 1.4 Are Steel-Frame Coasters Faster Than Wood-Frame Coasters Using IQR to Compare Samples How might you decide whether steel-frame coasters or wood frame coasters are faster?

Notes Using Mean, Median, IQR to compare roller coasters

Example pg 16 What do you consider to be a fast speed for a roller coaster? 60 or higher, like driving on the highway 2. Suppose you want to ride the faster of two roller coasters. Does knowing each roller coasters top speed help you make the decision? yes knowing speeds, choose the one with higher speeds Do you think steel-frame roller coasters are faster than wood-frame roller coasters? Use the top-speed data to justify you answer some wood are faster than steel but not all

B Identify the min and max values, ranges, means of each distribution. Use these stats to compare steel and wood 2. Identify the median and IQR of each, use these to compare the speeds Make a box and whisker plots of each

Part D Do you agree with Charlie or Rosa?

Homework You should be able to complete 9-16

Essential Questions Investigation 1.1 Given a set of results, how might you use measures of center and variability (spread) to judge overall performance? be able to compare mean, median and MAD to help determine similarities and differences Investigation 1.2 What strategies might you use to evaluate numerical outcomes and judge success? Use MAD to see how spread apart the data is Investigation 1.3 How might you compare results to see if each sample responds to a survey in a similar way? How can using percentages help you make comparisons? use mode which appears most often, use percentages to help make predictions, easier to compare a precent when totals for a question are different Investigation 1.4 How might you decide whether steel-frame coasters or wood frame coasters are faster? Use a box and whisker plot to look for percentages that are higher