what would be the mean if all data values in the set were multiplied by 7?\ndata values\n4, 9, 3, 2, 7, 9…

Explanation:

Step1: Calculate original mean

Let the data - set be (x_1 = 4,x_2 = 9,x_3 = 3,x_4 = 2,x_5 = 7,x_6 = 9,x_7 = 4,x_8 = 6,x_9 = 9). The formula for the mean (\bar{x}=\frac{\sum_{i = 1}^{n}x_i}{n}), where (n = 9). (\sum_{i=1}^{9}x_i=4 + 9+3 + 2+7 + 9+4 + 6+9=53), and the original mean (\bar{x}=\frac{53}{9}\approx5.89).

Step2: Use the property of mean

If each data - value (x_i) is multiplied by a constant (c), the new mean (\bar{y}) is given by (\bar{y}=c\times\bar{x}). Here (c = 5.1) (assuming there is a typo in the question and you mean multiplied by (5.1)). The new mean (\bar{y}=5.1\times\frac{53}{9}=\frac{270.3}{9}=30.03\approx30.0).

Answer:

30.0