Step 1 :Given the sample [50, 25, 34, 43, 34, 30, 44], subtract 20 from each item to get the new sample [30, 5, 14, 23, 14, 10, 24].
Step 2 :To find the mean of the new sample, sum all the numbers in the sample and then divide by the count of numbers in the sample.
Step 3 :The sum of the numbers in the new sample is \(30 + 5 + 14 + 23 + 14 + 10 + 24 = 120\).
Step 4 :The count of numbers in the new sample is 7.
Step 5 :So, the mean of the new sample is \( \frac{120}{7} = 17.142857142857142 \).
Step 6 :Rounding to the nearest hundredth, the mean of the new sample is 17.14.
Step 7 :Final Answer: The mean of the new sample is \( \boxed{17.14} \).