Use the table to answer the question.
Game Free Throws Made
1 4
2 14
3 5
4 7
5 19
6 15
7 6
What value, the mean or median, best describes the shape of the data set that contains the number of free throws made by the basketball team? Choose 1 for mean and 2 for median.
2 answers
2 (median)
To determine whether the mean or median better describes the shape of the data set for the number of free throws made, we need to consider the distribution of the values. If the data is symmetrically distributed, the mean and median will be similar. However, if there are outliers or the data is skewed, the median may be a better measure of central tendency because it is not affected by extreme values.
Let's calculate both:
The **mean** is the average of the numbers:
$$ \text{Mean} = \frac{4 + 14 + 5 + 7 + 19 + 15 + 6}{7} = \frac{70}{7} = 10 $$
The **median** is the middle value when the numbers are listed in order:
The ordered list is 4, 5, 6, 7, 14, 15, 19. The median value, which is the fourth value, is 7.
Given that the data set has a couple of high values (14, 15, and 19), which could skew the mean, the median might be a better representation of the central tendency of this data set.
Therefore, the answer is **2 for median**. It best describes the shape of the data set for the number of free throws made by the basketball team.
Let's calculate both:
The **mean** is the average of the numbers:
$$ \text{Mean} = \frac{4 + 14 + 5 + 7 + 19 + 15 + 6}{7} = \frac{70}{7} = 10 $$
The **median** is the middle value when the numbers are listed in order:
The ordered list is 4, 5, 6, 7, 14, 15, 19. The median value, which is the fourth value, is 7.
Given that the data set has a couple of high values (14, 15, and 19), which could skew the mean, the median might be a better representation of the central tendency of this data set.
Therefore, the answer is **2 for median**. It best describes the shape of the data set for the number of free throws made by the basketball team.
1 answer