Day 53 – Pennies’ Dates

Problem In what year was a typical penny currently in circulation minted, and how could you determine that year? Predict the year the typical penny currently in circulation was minted. How old is the typical penny? __________ : ___________ Minting Year Age Sort and stack your pennies into piles that were minted in the same year And put the piles in order from oldest to newest. Transfer the number of pennies in your piles to the dotplot with one x for each penny in that year. Leave empty columns for years with no pennies

Problem What can you say about the typical penny and its minting year or age from looking at the dotplot?

Problem Measures of Center IN WHAT YEAR WAS A TYPICAL PENNY MINTED? List the minting date of every penny in your data in sequence from newest to oldest to identify the extremes, quartiles, and median. Check for any possible outliers. Then make a boxplot of the data. Use the diagram and table on page 5 complete your list and boxplot. Measures of Center What is the mean of the minting dates of your pennies? ..median? 2. Where do you see these on the dotplot?

Problem 3. What do these tell you about pennies currently in circulation? 4. Which do you think is the best measure of center? Why?

Problem Measures of Variability What is the standard deviation of the minting dates of your pennies? ..interquartile range? 2. What do these tell you about pennies currently in circulation? 3. Which do you think is the best measure of variability? Why?

Problem Dotplots 1. What patterns do you see in the heights on the dotplot? 2. What does that tell you about these pennies? 3. How does your data compare to the data of other groups?

Problem 1. How much of the boxplot is made of just the box? Boxplot – In the grids on the following page, list the minting date of every penny in your data in sequence from newest to oldest to identify the extremes, quartiles, and median. Then make a box- and-whisker plot of the data. 1. How much of the boxplot is made of just the box? 2. What fraction of the pennies does the box represent?

Problem 3. Why is half the data filling much less than half the plot? 4. Did you have any outliers?

Problem 5. How do the two whiskers of the plot compare in length? 6. What fraction of the pennies does each whisker represent?

Problem 7. Since the whiskers are different lengths but represent the same amount of data, what does that tell you about the pennies in the longer whisker? 8. Summarize what the boxplot tells you about the minting dates of pennies.

Problem(answer) What can you say about the typical penny and its minting year or age from looking at the dotplot? Answers will vary Measures of Center What is the mean of the minting dates of your pennies? ..median? Answers may vary 2. Where do you see these on the dotplot? Answers may vary 3. What do these tell you about pennies currently in circulation? Answers may vary 4. Which do you think is the best measure of center? Why? Answers may vary

Problem(answer) Measures of Variability 1. What is the standard deviation of the minting dates of your pennies? ..interquartile range? Answers may vary 2. What do these tell you about pennies currently in circulation? Answers may vary 3. Which do you think is the best measure of variability? Why? Answers may vary

Problem(answer) Dotplots 1. What patterns do you see in the heights on the dotplot? Answers may vary 2. What does that tell you about these pennies? Usually as the year goes up, the number of pennies go up. 3. How does your data compare to the data of other groups? It is a positive trend.

Problem(answer) 1. How much of the boxplot is made of just the box? 50% 2. What fraction of the pennies does the box represent? ½ 3. Why is half the data filling much less than half the plot? The number are closer together 4. Did you have any outliers? Answer may vary 5. How do the two whiskers of the plot compare in length? Usually – the left is longer than the right. 6. What fraction of the pennies does each whisker represent? ¼ 7. Since the whiskers are different lengths but represent the same amount of data, what does that tell you about the pennies in the longer whisker? The dates are most spread out 8. Summarize what the boxplot tells you about the minting dates of pennies. Answers may vary