520: Dan or Mike? Who's Better at Doodle Jump?

Every year I give this graphic comparing the Doodle Jump stats for @ddmeyer and his friend Mike.


Give a couple of reasons why we could consider Dan the better player.
Give a couple of reasons why we could consider Mike the better player.

Measures of Central Tendency.

321: Sensible or Not? central measures

Measures of Central Tendency Statements: Sensible or Not?
Defend your answer! Here's your claim ... what's your warrant?
Give an example or a situation to bolster your position 

1. A data set should be discarded if the mean exceeds the mode. 
2. A student with an average of 65 computes her new average after earning a 70 on the last exam. Her new average is 72. 
3. Observing that the mean weight of a group of patients is 154 pounds and the median weight is 145 pounds, the doctor concludes that there must be an outlier on the heavy side. 
4. Noting that there are three modes in his data set, Rob assumes there was an error in his data gathering. 
5. The two means in the data lie at 102 and 201
6. The two medians in the data set lie at 23 and 28. 
7. The two modes in the data set lie at 45 and 100. 

ch4.1

277: Central Tendency Mistakes

Expand that image to see details. As you peruse the list of values, how far can you get before you reach an inconsistency? Can we figure out what date each of the five pennies showed?

If you knew this was from a college teacher-education professor, would this change your opinion of the work shown in the picture?

249: Create some data

Can you create a set of data (more than 12 numbers, please) with a mean of 17 and a median of -17 and a mode of 0?

248: Raising one out of two.

Can you create a data set of more than 5 numbers so that when you add one additional number to the set, you can raise the median but not the mean?

241: Mode not Median

Given the same numbers as we've been working with for a couple of days, along with an extra number X:

X, 12783, 12784, 12785, 12790, 12792, 12795, 12799, 12801 

What values can X take on so that it is the mode but not the median?

240: Median not Average

Given the same numbers as we've been working with for a couple of days, along with an extra number X:

X, 12783, 12784, 12785, 12790, 12792, 12795, 12799, 12801 

What values can X take on so that it is the median but not the average?

239: Outliers

Given the same numbers as we've been working with for a couple of days, along with an extra number X:

X, 12783, 12784, 12785, 12795, 12792, 12790, 12799, 12801 

How small (or large) do you feel that value of x should be to be considered an outlier?

and of course, Ben Shabad, full-time graduate student and part-time cartoon-drawing person.

238: Skew

Given the same numbers as yesterday:

12783, 12784, 12785, 12790, 12792, 12795, 12799, 12811 

What characteristics can we look at to tell whether this data is skewed?

237: Average

Given the numbers:

12783, 12784, 12785, 12795, 12792, 12790, 12799, 12801 

There are a lot of tricks and shortcuts, and of course, the pencil and paper add-em-up method of finding the average of a set of numbers.
What's your best way to get the average of those eight numbers?

135: Raising the Average

In a charter school of 400 students, the average score on a standardized test at the beginning of the year was 82%.

By the end of the first few months, 92 students couldn't take it anymore: the 9-hour days of which 8.5 hours were spent staring at computer screens, the required Saturday classes and the constant badgering over being quiet, walking dully in a single file, drill, drill, drill, drill, and drill, all seemingly in an effort to get them to drop out.

The 92 students, who were getting Ds and Fs, had a collective average of 60, which is why they were targeted.

In late October, Jay Matthews of the Washington Post interviews the principal for a Thanksgiving-themed piece in the paper and asked about the gains and improvements that the wonderful charter-school had been able to accomplish.

The principal did not mention that the students had not taken the test again or that the rise was simply because of the elimination of what he considered inferior students.  Instead, the principal said proudly, "Our program is amazing. We have been able to raise their scores by _________ in just two months. If the City gives over some more public schools to our control, we'll be able to do more of this."

How much did scores rise because of the expulsion/removal of the 92 lower-scoring students?

Q7 - The Mean and Hidden Information

Question 7: Most teachers use the mean to assign a grade, but this measure hides information. What information is hidden and what, if anything, should we do about it?