Question

ms. monroe mixes 200 cubes of 4 different colors for a project. she then uses a scoop to place 20 cubes into each of 10 paper bags. each group records the number of cubes of each color in a bag. the number of red cubes for the 10 groups are recorded in the graph. which statement is true about the mean and median of the numbers of red cubes in the bags? the mean number of red cubes is less than the median number of red cubes. the mean number of red cubes is more than the median number of red cubes. the mean number of red cubes is equal to the median number of red cubes. the mean number of red cubes cannot be compared to the median number of red cubes.

Explanation:

Step1: List the data values

The data points from the dot - plot are: 0, 1, 2, 3, 4, 6, 7, 8, 9, 10.

Step2: Calculate the mean

The mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, where $n = 10$ and $\sum_{i=1}^{10}x_{i}=0 + 1+2 + 3+4+6+7+8+9+10=50$. So, $\bar{x}=\frac{50}{10}=5$.

Step3: Calculate the median

Since $n = 10$ (an even number), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. The $\frac{10}{2}=5$th value is 4 and the $(\frac{10}{2}+1)=6$th value is 6. So, the median $M=\frac{4 + 6}{2}=5$.

Answer:

The mean number of red cubes is equal to the median number of red cubes.