Question

1. is the mean greater than, less than, or equal to the median? greater than less than equal to

Explanation:

Step1: Count data - points

Count the number of dots in the dot - plot. There are 10 values at each of the 9 positions, so there are \(n = 9\times10=90\) data - points.

Step2: Find the median position

For a set of \(n = 90\) data - points (an even number of data - points), the median is the average of the \(\frac{n}{2}=45\)th and \((\frac{n}{2}+1) = 46\)th ordered data - points. When we order the data, the 45th and 46th values fall in the 25 value category. So the median is 25.

Step3: Calculate the mean

Let \(x_i\) be the values on the x - axis (\(x_1 = 10,x_2 = 15,\cdots,x_9 = 50\)) and \(f_i = 10\) for \(i = 1,\cdots,9\). The mean \(\bar{x}=\frac{\sum_{i = 1}^{9}f_ix_i}{\sum_{i = 1}^{9}f_i}\). \(\sum_{i = 1}^{9}f_ix_i=10\times(10 + 15+20 + 25+30+35+40+45+50)=10\times(10 + 50)\times\frac{9}{2}=10\times270 = 2700\), and \(\sum_{i = 1}^{9}f_i=90\). So \(\bar{x}=\frac{2700}{90}=30\).

Step4: Compare mean and median

Since \(30>25\), the mean is greater than the median.

Answer:

greater than