Calculator

Practical Example

Let’s suppose we have a product with the following details:

  • Current Average = 3.93
  • Current Count = 57
  • Desired Average = 4.5

Plugging those values into the equation:

x = ( 4.5 − 3.93 ) × 57 5 − 4.5

Let’s calculate it:

x = 0.57 × 57 0.5 = 32.49 0.5 = 64.98

And since you can’t have a fraction of a rating, you would need at least 65 additional 5-star ratings to reach an average of 4.5.

Math Explanation

To determine the number of additional 5-star ratings you need to achieve a desired average rating, we use simple algebra. Here’s a step-by-step explanation:

1. Define the Variables:

  • Let Current Average be the current average rating.
  • Let Current Count be the current number of ratings.
  • Let Desired Average be the desired average rating.
  • Let x be the number of additional 5-star ratings needed.

2. Set up the Equation

  • The total sum of the ratings currently is Current Average × Current Count
  • The total sum of the ratings after adding x more 5-star ratings will be: ( Current Average × Current Count ) + ( 5 × x )
  • The total number of ratings after adding x more ratings will be Current Count+ x

3. Create the Equation:

Now in order to get the Desired Average, we use the following equation:

Desired Average = ( Current   Average  ×  Current   Count )  +  ( 5  ×  x ) Current   Count  +  x

4. Solve for x:

  • Multiply both sides by Current Average + x to clear the denominator: Desired Average × ( Current Average + x ) = ( Current Average × Current Count ) + ( 5 × x )
  • Expand and rearrange to solve for x: Desired Average × Current Count + Desired Average × x = Current Average × Current Count + 5x
  • Combine like terms: Desired Average × Current Count − Current Average × Current Count = 5x − Desired Average × x

    • Then:

    (Desired Average − Current Average)× Current Count = x(5−Desired Average)
  • Finally, solve for x: x = ( Desired   Average  -  Current   Average )  ×  Current   Count 5  -  Desired   Average

And that is how we get the number of ratings needed to achieve a desired rating.