IM Alg1.1.10 Lesson: The Effect of Extremes

Several video games are based on a genre called "Battle Royale" in which 100 players are on an island and they fight until only 1 player remains and is crowned the winner.

[size=150]This type of game can often be played in solo mode as individuals or in team mode in groups of 2.[br][br][/size][size=100]What information would you use to determine the top players in each mode (solo and team)? Explain your reasoning.[/size][size=150][br][/size]

[size=100]One person claims that the best solo players play game A. Another person claims that game B has better solo players. How could you display data to help inform their discussion? Explain your reasoning.[/size][br]

Use the applet to create a dot plot that represents the distribution of the data.

Describe the shape of the distribution.

[list][/list]Find the mean and median of the data.

Find the mean and median of the data with 2 additional values included as described.

Add 2 values to the original data set that are greater than 14.

[list][/list][left]Add 2 values to the original data set that are less than 6.[br][/left]

[list][/list][left]Add 1 value that is greater than 14 and 1 value that is less than 6 to the original data set.[/left]

[list][/list][left]Add the two values, 50 and 100, to the original data set.[/left]

[list][/list][left]Change the values so the distribution fits the description given to you by your teacher, then find the mean and median.[/left]

[list][/list][left]Find another group that created a distribution with a different description. Explain your work and listen to their explanation, then compare your measures of center.[/left]

Create a possible dot plot with at least 10 values for a distribution that has both mean and median of 10. Each dot plot must have at least 3 values that are different.

Create a possible dot plot with at least 10 values for a distribution that has both mean and median of -15. Each dot plot must have at least 3 values that are different.

Create a possible dot plot with at least 10 values for a distribution that has a median of 2.5 and a mean greater than the median. Each dot plot must have at least 3 values that are different.

Create a possible dot plot with at least 10 values for a distribution that has a median of 5 and a median greater than the mean. Each dot plot must have at least 3 values that are different.

The mean and the median are by far the most common measures of center for numerical data.

[size=150]There are other measures of center, though, that are sometimes used. For each measure of center, list some possible advantages and disadvantages. Be sure to consider how it is affected by extremes.[br][br][/size][size=100][i]Interquartile mean[/i]: The mean of only those points between the first quartile and the third quartile.[/size]

[i]Midhinge[/i]: The mean of the first quartile and the third quartile.

[i]Midrange[/i]: The mean of the minimum and maximum value.

[i]Trimean[/i][i]:[/i] The mean of the first quartile, the median, the median again, and the third quartile. So we are averaging four numbers as the median is counted twice.