Question

what would be the mean if all data values in the set were multiplied by 7?
data values
4, 9, 3, 2, 7, 9, 4, 6, 9
30.0
29.4
10.9
5.9

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