Question

Christina collected information about the ages of the players on her softball team. The ages were 10, 12, 14, 13, 12, 11, 13, 12, 11, 12, 12, and 13. Christina wants to describe the players’ ages in an article for the school newspaper. She does not want to list all of the ages, so should she use the range (difference between the highest and lowest values) or a measure of central tendency (mean, median) to describe them? Justify your choice.

Answer 1

We are told that Christina collected information about the ages of the players on her softball team. The ages were 10, 12, 14, 13, 12, 11, 13, 12, 11, 12, 12, and 13. Christina wants to describe the players’ ages in an article for the school newspaper.

Since we know that range of a data is difference between the highest and lowest values of a data set. Range of our data set will be 4 (14-10). A group of different ages could have same range as Christina's data set. So range will be not a good option.

A measure of central tendencies will be better option to represent information about ages of softball team players. Mean will give the average age of softball players.

$\text{Mean age of players}=\frac{10+11+11+12+12+12+12+12+13+13+13+14}{12}$

$\text{Mean age of players}=\frac{145}{12}=12.0833$

Let us find median of data.

10,11,11,12,12,12,12,12,13,13,13,14        

$\text{Median age of softball players}=\frac{12+12}{2}$

$\text{Median age of softball players}=\frac{24}{2}=12$

We can see that average of our data is 12 years.    

Therefore, a measure of central tendency will be better choice to describe ages of softball players.