Given the frequency distribution table with intervals: 1-10, 11-20, 21-30, 31-40, 41-50 and corresponding frequencies of: 5, 15, 20, 7, 3. What are the midpoints of each interval, and what is the midpoint of the frequency distribution table?
Solution
Step 1 ：Step 1: Calculate the midpoint of each interval. The midpoint is given by \((lower\ limit + upper\ limit)/2\). So, for intervals 1-10, 11-20, 21-30, 31-40, 41-50 we have midpoints of \(5.5\), \(15.5\), \(25.5\), \(35.5\), \(45.5\) respectively.
Step 2 ：Step 2: Multiply each midpoint by its corresponding frequency. So, we have: \(5.5*5\), \(15.5*15\), \(25.5*20\), \(35.5*7\), \(45.5*3\) which results in: \(27.5\), \(232.5\), \(510\), \(248.5\), \(136.5\) respectively.
Step 3 ：Step 3: Add up all the values from the previous step to get the sum of all midpoints multiplied by their frequencies, which is: \(27.5+232.5+510+248.5+136.5 = 1155\).
Step 4 ：Step 4: Add up all the frequencies to get the total frequency, which is: \(5+15+20+7+3 = 50\).
Step 5 ：Step 5: Divide the sum of all midpoints multiplied by their frequencies by the total frequency to get the midpoint of the frequency distribution table, which is: \(1155/50\).
