Warm Up! Write down objective and homework in agenda Lay out homework (MOC: Mean wkst) Homework (MOC: Median wkst)

Unit 2 Common Core Standards MP.1 Make sense of problems and persevere in solving them. MP.2 Reason abstractly and quantitatively. MP.3 Construct viable arguments and critique the reasoning of others. MP.4 Model with mathematics. MP.5 Use appropriate tools strategically. MP.6 Attend to precision. N-Q.1 Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N-Q.2 Define appropriate quantities for the purpose of descriptive modeling. N-Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities. S-ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots). 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. S-ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).

Warm Up Use intervals of 10

Warm Up Answers

Vocabulary Measures of Center What is the typical value? Today we will focus more on the Median!

Investigation 1: Dotplots vs. Histograms

Examine the two plots. Describe the distribution of the data in context (shape, center, spread, outliers). How are the two graphs alike? How are they different? How can you use each graph to determine the total number of letters in all the names? Cassandra Smithson said, “My name has the most letters, but the bar that shows my name length is one of the shortest on the graph. Why?” How would you answer this question?

Describing Data Two ways to describe data: Graphically Dot plot Histogram – Boxplot Numerically – Measures of Center – Measures of 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.

Investigation 3: Experimenting With the Median Name Number of Letters Thomas Petes11 Michelle Hughes14 Shoshana White13 Deborah Black12 Tonya Stewart12 Richard Mudd11 Tony Tung8 Janice Wong10 Bobby King9 Charlene Green13 Richard Mudd 11 letters

Investigation 3 Order the names from shortest name length to longest name length, and identify the median of the data. Remove two names from the original data set so that: – the median stays the same. What names did you remove? – the median increases. What names did you remove? – the median decreases. What names did you remove?

Investigation 3 Now, ADD two names to the original data set so that: – the median stays the same. What names did you add? – the median increases. What names did you add? – the median decreases. What names did you add? How does the median of the original data set change if you add – a name with 16 letters? – a name with 4 letters? – the name William Arthur Philip Louis Mountbatten- Windsor (a.k.a. Prince William) to the list?

Investigation 3 Make a histogram on the calculator using the data Describe the distribution – Closely Pay Attention to the Mean and Median as you Describe the Center when describing your data set with details

How do I know which measure of central tendency to use?

Did you Know….. Names from many parts of the world have special origins. European family names (last names) often came from the father’s first name. For example, Ian Robertson was the son of Robert, Janos Ivanovich was the son (vich) of Ivan, and John Peters was the son of Peter. Family names also came from words that described a person’s hometown or job. This resulted in such names and William Hill and Gilbert Baker. Family names in China and Vietnam are almost always one-syllable words that are related to names of ruling families. Chang is one such example.