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

There are 10 values at each of the following: 10, 15, 20, 25, 30, 35, 40, 45, 50. So there are a total of \(10\times9 = 90\) data - points.

Step2: Calculate the median

Since \(n = 90\) (an even number), the median is the average of the \(\frac{n}{2}=45\)th and \((\frac{n}{2}+ 1)=46\)th ordered data - points. Counting the data - points from the left, both the 45th and 46th data - points are 30. So the median \(M = 30\).

Step3: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{9}x_{i}f_{i}}{\sum_{i = 1}^{9}f_{i}}\), where \(x_{i}\) are the values on the number - line (\(x_1 = 10,x_2 = 15,\cdots,x_9 = 50\)) and \(f_{i}=10\) for \(i = 1,\cdots,9\).
\(\sum_{i = 1}^{9}x_{i}f_{i}=10\times(10 + 15+20 + 25+30+35+40+45+50)=10\times\frac{(10 + 50)\times9}{2}=10\times270 = 2700\).
\(\sum_{i = 1}^{9}f_{i}=90\). So \(\bar{x}=\frac{2700}{90}=30\).

Answer:

equal to