Question

1. write and solve an equation to find the value of the variable.

5.2, 8.3, 8.5, 7.7, 7.8, y; mean = 7.1

5.1

5.8

5.9

5.3

Explanation:

Step1: Recall the formula for the mean

The formula for the mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$. Here, $n = 6$ (since there are 6 numbers: $5.2,8.3,8.5,7.7,7.8,y$), and $\bar{x}=7.1$. So, $7.1=\frac{5.2 + 8.3+8.5 + 7.7+7.8+y}{6}$.

Step2: Simplify the numerator of the right - hand side

First, calculate $5.2+8.3+8.5+7.7+7.8=(5.2 + 8.3)+(8.5+7.7)+7.8=13.5+16.2 + 7.8=13.5+(16.2+7.8)=13.5 + 24=37.5$. The equation becomes $7.1=\frac{37.5 + y}{6}$.

Step3: Solve the equation for $y$

Multiply both sides of the equation by 6: $7.1\times6=37.5 + y$. Then, $42.6=37.5 + y$. Subtract 37.5 from both sides: $y=42.6-37.5$.

Step4: Calculate the value of $y$

$y = 5.1$.

Answer:

$5.1$