High School

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Find the mean of the following distribution:

Classes: 10-25, 25-40, 40-55, 55-70, 70-85, 85-100
Frequencies: 2, 3, 7, 6, 6, 6

Answer :

Final answer:

To find the mean of the distribution, calculate the midpoint for each class, multiply each midpoint by its corresponding frequency, sum these products, and then divide by the total frequency. The mean of this particular distribution is 62.

Explanation:

To find the mean of the given distribution, we first need to calculate the midpoint (also known as the class mark) of each class, which is the average of the upper and lower boundaries of that class. Then, we multiply each midpoint by its corresponding frequency to find the weighted sum. Finally, we divide this sum by the total frequency to get the mean.

  • Classes: 10-25, 25-40, 40-55, 55-70, 70-85, 85-100
  • Frequencies: 2, 3, 7, 6, 6, 6

Step-by-step calculation:

  1. Calculate midpoints: (10+25)/2=17.5, (25+40)/2=32.5, (40+55)/2=47.5, (55+70)/2=62.5, (70+85)/2=77.5, (85+100)/2=92.5
  2. Multiply each midpoint by its frequency: 17.5*2=35, 32.5*3=97.5, 47.5*7=332.5, 62.5*6=375, 77.5*6=465, 92.5*6=555
  3. Add the products: 35+97.5+332.5+375+465+555=1860
  4. Total frequency: 2+3+7+6+6+6=30
  5. Divide the sum of products by the total frequency: 1860/30 = 62

The mean of the distribution is 62.

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