If is the mean of 10 observations ; then what is the value of ?

112. Since the mean for 10 observations, the sum of the observations is . We need to evaluate . This gives .

If \overline{X}=20 is the mean of 10 observations X_1, X_2, \dots, X_{10}; then what is the value of \sum_{i=1}^{10}\left(\frac{3X_i-4}{5}\right)?

A. 0
B. 12
C. 112 ✓
D. 1012

Correct Answer: C. 112

Explanation

Since the mean \overline{X} = 20 for 10 observations, the sum of the observations is \sum X_i = 10 \times 20 = 200. We need to evaluate \sum_{i=1}^{10} \left(\frac{3X_i}{5} - \frac{4}{5}\right) = \frac{3}{5}\sum X_i - \sum \frac{4}{5}. This gives \frac{3}{5}(200) - \frac{4}{5}(10) = 120 - 8 = 112.

If \overline{X}=20 is the mean of 10 observations X_1, X_2, \dots, X_{10}; then what is the value of \sum_{i=1}^{10}\left(\frac{3X_i-4}{5}\right)?

Explanation

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