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. red cubes per bag 0 1 2 3 4 5 6 7 8 9 10 number of red cubes in each bag

Explanation:

Step1: List the data values

From the dot - plot, the number of red cubes in the 10 bags are (let's assume the dots represent the following values in order): 0, 0, 1, 1, 2, 2, 3, 3, 8, 9.

Step2: Calculate the median

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

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data - points and \(n = 10\). \(\sum_{i=1}^{10}x_{i}=0 + 0+1 + 1+2 + 2+3 + 3+8 + 9=29\), and \(\bar{x}=\frac{29}{10}=2.9\).

Step4: Compare the mean and median

Since \(2.9>2\), the mean number of red cubes is more than the median number of red cubes.

Answer:

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