Question

ten students wrote a test, and the distribution of scores is shown on the frequency table. if the average (arithmetic mean) score is 62, what is the value of x?

choose the option that best answers the question.

Explanation:

Step1: Calculate the total score

The formula for the arithmetic mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}f_{i}}{\sum_{i = 1}^{n}f_{i}}$. Here, $\sum_{i = 1}^{n}f_{i}=1 + 2+3 + 4=10$. And $\sum_{i = 1}^{n}x_{i}f_{i}=40\times1 + 55\times2+70\times3+4x$.

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Step2: Use the mean formula

Since the mean $\bar{x} = 62$ and $\sum_{i = 1}^{n}f_{i}=10$, $\sum_{i = 1}^{n}x_{i}f_{i}=62\times10 = 620$.
We have the equation $360+4x=620$.
Subtract 360 from both sides: $4x=620 - 360$.

$$ 4x=260 $$

Divide both sides by 4: $x=\frac{260}{4}=65$.

Answer:

65