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. red cubes per bag 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 out the data

The number of red - cubes in the 10 bags (from the dot - plot) are: 0, 0, 1, 2, 3, 4, 6, 7, 8, 9.

Step2: Calculate the median

Since there are \(n = 10\) data points (an even number of data points), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered data points. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5th value is 3 and the 6th value is 4. So, the median \(M=\frac{3 + 4}{2}=3.5\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data - points and \(n = 10\). \(\sum_{i=1}^{10}x_{i}=0+0 + 1+2+3+4+6+7+8+9=40\). So, the mean \(\bar{x}=\frac{40}{10}=4\).

Answer:

The mean number of red cubes is more than the median number of red cubes.