Question

1. the data set and dot plot display the number of questions a student missed on 10 math quizzes. what is a correct description of the distribution?

3\t0\t2\t3\t6
2\t4\t3\t3\t4
dot plot with 0:1 dot, 2:2 dots, 3:4 dots, 4:2 dots, 6:1 dot
a the data is skewed; the measures of center are varied.
b the data is skewed; the measures of center are equal.
c the data is normal; the measures of center are varied.
d the data is normal; the measures of center are equal.

Explanation:

Step1: Analyze data distribution

First, let's list out the data: 0, 2, 2, 3, 3, 3, 3, 4, 4, 6. A normal distribution is symmetric, but here we have a value (6) that is far from the main cluster, and the left side (around 0 - 4) has more data. So the data is skewed (right - skewed because of the tail at 6).

Step2: Calculate measures of center

• Mean: Sum the data: \(0 + 2+2 + 3+3+3+3 + 4+4 + 6=\frac{0 + 2\times2+3\times4 + 4\times2+6}{1}=\frac{0 + 4+12 + 8+6}{1}=32\). Mean \(=\frac{32}{10} = 3.2\).
• Median: Since there are 10 data points (even), the median is the average of the 5th and 6th terms. The 5th term is 3, the 6th term is 3. Median \(=\frac{3 + 3}{2}=3\).
• Mode: The number that appears most often is 3 (appears 4 times).

The mean (\(3.2\)), median (\(3\)), and mode (\(3\)) are not all equal, so the measures of center are varied. And the data is skewed (not normal, as normal data is symmetric and has mean = median = mode approximately). So the correct description is that the data is skewed; the measures of center are varied.

Answer:

A. The data is skewed; the measures of center are varied.