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 = \frac{(4.5 - 3.93) \times 57}{5 - 4.5}

Let’s calculate it:

x = \frac{0.57 \times 57}{0.5} = \frac{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 $Current Average \times Current Count$
The total sum of the ratings after adding $x$ more 5-star ratings will be: $(Current Average \times Current Count) + (5 \times x)$
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 = \frac{(Current Average \times Current Count) + (5 \times x)}{Current Count + x}

4. Solve for $x$ :

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

Then:

(Desired Average - Current Average) \times Current Count = x (5 - Desired Average)

Finally, solve for $x$ : $x = \frac{(Desired Average - Current Average) \times Current Count}{5 - Desired Average}$

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