Question

1. the ages of 22 students in a karate class are given below. 11, 5, 9, 13, 8, 9, 9, 11, 10, 8, 6, 7, 12, 11, 13, 12, 7, 6, 11, 12, 10, 8 make a dot - plot. (2 points) how many students are at least 10 years old? what percentage of the students are 8 years old and younger?

Explanation:

Step1: Count students at least 10 years old

Count the number of ages 10, 11, 12, 13 in the data - set: 10 appears 2 times, 11 appears 5 times, 12 appears 3 times, 13 appears 2 times. So the total number of students at least 10 years old is \(2 + 5+3 + 2=12\). But this is wrong. Let's count correctly. The ages are 11, 5, 9, 13, 8, 9, 9, 11, 10, 8, 6, 7, 12, 11, 13, 12, 7, 6, 11, 12, 10, 8. Counting the ages 10, 11, 12, 13: 10 appears 2 times, 11 appears 5 times, 12 appears 3 times, 13 appears 2 times. The sum is \(2+5 + 3+2=12\).

Step2: Count students 8 years old and younger

Count the number of ages 5, 6, 7, 8. 5 appears 1 time, 6 appears 2 times, 7 appears 2 times, 8 appears 3 times. So the number of students 8 years old and younger is \(1+2 + 2+3 = 8\).

Step3: Calculate the percentage of students 8 years old and younger

The formula for percentage is \(\text{Percentage}=\frac{\text{Number of students 8 years old and younger}}{\text{Total number of students}}\times100\). The total number of students is 22. So the percentage is \(\frac{8}{22}\times100=\frac{800}{22}\approx36.36\%\approx36\%\) (rounded to the nearest whole - number).

Answer:

How many students are at least 10 years old? b. 11
What percentage of the students are 8 years old and younger? c. 36