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 number of red cubes in each 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: Count data - points

There are 10 data - points (number of bags). The data values from the dot - plot are: 1, 1, 3, 3, 3, 3, 5, 7, 7, 9.

Step2: Calculate the median

Since \(n = 10\) (even), the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+1)\)th ordered values. \(\frac{n}{2}=5\) and \(\frac{n}{2}+1 = 6\). The 5th value is 3 and the 6th value is 3. So, median\(=\frac{3 + 3}{2}=3\).

Step3: Calculate the mean

Mean\(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\), where \(x_{i}\) are the data values and \(n = 10\). \(\sum_{i=1}^{10}x_{i}=1+1 + 3+3+3+3+5+7+7+9=42\). Mean\(=\frac{42}{10}=4.2\).

Step4: Compare mean and median

Since \(4.2>3\), 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.