A store receives customer satisfaction ratings on a scale of 1-50 (both inclusive). In the first five ratings the store received an average rating of 27. What is the least value the Store can receive on the 6^{th} rating and still be able to have an average of at least 35 in the first 10 ratings?

**Solution:**

Since, the first five ratings received an average rating of 27.

Therefore, sum of the first 5 ratings = 5 * 27 (as Average = Sum of observation / Number of observations) = 135.

In order for average to be at least 35 for the first 10 ratings, the sum of the ratings should be at least 35 * 10 = 350

Hence the sum of observations (6^{th} to 10^{th}) must be at least 350 – 135 = 215.

Also, our objective is to find the least value for 6^{th} customer rating.

Therefore, we need to maximize 7^{th}, 8^{th}, 9^{th} and 10^{th} rating.

The maximum value of any rating can be 50. (given in the question)

Therefore, least value of 6^{th} rating will be as follows

6^{th} rating + 4(50) = 215

Hence 6^{th} rating minimum value will be **15.**