Question

1. the preceding dot plot displays the scores of 20 students on a science exam. the standard deviation of these data is approximately 13.2. determine the number of students whose scores are within 1 standard deviation of the mean.

a 11
b 12
c 13
d 14

Explanation:

Step1: Calculate the mean

From the dot - plot, we can calculate the mean \(\bar{x}\).

$$
LATEXBLOCK0
$$

Step2: Determine the range within 1 standard deviation of the mean

The range is \(\bar{x}-s\) to \(\bar{x} + s\), where \(s = 13.2\). So the range is \(65−13.2=51.8\) to \(65 + 13.2=78.2\)

Step3: Count the number of data points in the range

Count the number of dots (students' scores) between \(51.8\) and \(78.2\) on the dot - plot.
From the dot - plot:

• Scores of \(55\): \(2\) students
• Scores of \(60\): \(3\) students
• Scores of \(65\): \(3\) students
• Scores of \(70\): \(2\) students
• Scores of \(50\): \(2\) students (since \(50>51.8\))

The total number of students \(=2 + 3+3+2+2=12\)

Answer:

B. 12