Question

a group of high school students worked part - time jobs over the summer. their weekly earnings are shown in the dot plot. what is the median of their earnings? options (vertical boxes): $130, $150, $180, $153

Explanation:

Step1: Count the number of data points

First, we count the number of dots in the dot - plot. Let's list out the number of dots for each wage:

• For $130: 1$ dot.
• For $140: 2$ dots.
• For $150: 3$ dots.
• For $160: 2$ dots.
• For $170: 1$ dot.
• For $180: 1$ dot.

The total number of data points $n=1 + 2+3 + 2+1 + 1=10$.

Step2: Determine the position of the median

For a set of data with $n$ values, if $n$ is even, the median is the average of the $\frac{n}{2}$ - th and $(\frac{n}{2}+1)$ - th values when the data is ordered from least to greatest.

Since $n = 10$ (even), we need to find the average of the $\frac{10}{2}=5$ - th and $(\frac{10}{2}+1)=6$ - th values.

Step3: Order the data and find the 5th and 6th values

Let's order the data by listing the wages in ascending order:

• $130$ (1st)
• $140,140$ (2nd, 3rd)
• $150,150,150$ (4th, 5th, 6th)
• $160,160$ (7th, 8th)
• $170$ (9th)
• $180$ (10th)

The 5th value is $150$ and the 6th value is $150$.

Step4: Calculate the median

The median is the average of the 5th and 6th values. So, median $=\frac{150 + 150}{2}=\frac{300}{2}=150$.

Answer:

$\$150$