Question

1. find the mean, variance, and standard deviation for the following data.

1. find abbys overall grade(to the nearest percent) in government class if her grade is weighted using the following weights.

Explanation:

Step1: Calculate the weighted mean

The formula for the weighted mean is \(\bar{x}=\sum_{i = 1}^{n}w_ix_i\), where \(w_i\) is the weight and \(x_i\) is the value.
For homework: \(w_1 = 0.2\), \(x_1=95\), so \(w_1x_1=0.2\times95 = 19\)
For quizzes: \(w_2 = 0.3\), \(x_2 = 84\), so \(w_2x_2=0.3\times84=25.2\)
For tests: \(w_3 = 0.4\), \(x_3 = 78\), so \(w_3x_3=0.4\times78 = 31.2\)
For current events: \(w_4=0.1\), \(x_4 = 100\), so \(w_4x_4=0.1\times100 = 10\)

Step2: Sum up the weighted values

\(\bar{x}=19 + 25.2+31.2 + 10\)
\(\bar{x}=85.4\)

Answer:

\(85\) (rounded to the nearest percent)