To find the mean of the given data set, you follow these steps:
- Sum all the values.
- Divide the sum by the number of values.
Let's calculate it step-by-step.
Values: \( 34, 45, 50, 56, 60, 65, 70, 70, 70, 70, 72, 77, 77, 80, 82, 86, 86, 89, 95, 98 \)
Step 1: Calculate the sum:
\[ 34 + 45 + 50 + 56 + 60 + 65 + 70 + 70 + 70 + 70 + 72 + 77 + 77 + 80 + 82 + 86 + 86 + 89 + 95 + 98 = 34 + 45 = 79 \ 79 + 50 = 129 \ 129 + 56 = 185 \ 185 + 60 = 245 \ 245 + 65 = 310 \ 310 + 70 = 380 \ 380 + 70 = 450 \ 450 + 70 = 520 \ 520 + 70 = 590 \ 590 + 72 = 662 \ 662 + 77 = 739 \ 739 + 77 = 816 \ 816 + 80 = 896 \ 896 + 82 = 978 \ 978 + 86 = 1064 \ 1064 + 86 = 1150 \ 1150 + 89 = 1239 \ 1239 + 95 = 1334 \ 1334 + 98 = 1432 \]
Total Sum = 1432
Step 2: Count the number of values:
There are 20 values in the data set.
Step 3: Calculate the mean:
\[ \text{Mean} = \frac{\text{Total Sum}}{\text{Number of Values}} = \frac{1432}{20} = 71.6 \]
So, the mean of the given data set is 71.6.