Question

1. a class of students was surveyed to determine the number of pets each student owned. the data are represented in the dot - plot below. number of pets a) what is the median number of pets? b) what is the most common number of pets owned by each student in the class? c) how many students were surveyed? 4) using the data above, fill out the five number summary below and then create a box plot to summarize the data. minimum q1 median q3 maximum

Explanation:

Step1: Count data - points

Count the number of dots in the dot - plot. There is 1 dot at 0, 4 dots at 1, 7 dots at 2, 5 dots at 3, 2 dots at 4, and 1 dot at 5. So, the total number of students surveyed is $1 + 4+7 + 5+2 + 1=20$.

Step2: Find the median position

Since $n = 20$ (an even number), the median is the average of the $\frac{n}{2}=10$th and $(\frac{n}{2}+ 1)=11$th ordered data - values. Counting the dots: 1 (at 0) + 4 (at 1) = 5, and 5+7 (at 2) = 12. So, the 10th and 11th values are both 2, and the median is 2.

Step3: Find the mode

The mode is the value with the most number of dots. The number 2 has 7 dots, which is more than any other number, so the mode is 2.

Step4: Find the five - number summary

• Minimum: The smallest value in the data set is 0.
• Q1: The lower half of the data has $n_1 = 10$ values. The median of the lower half is the average of the 5th and 6th values. Since 1 (at 0) + 4 (at 1) = 5, the 5th and 6th values are 1, so $Q1 = 1$.
• Median: We already found it to be 2.
• Q3: The upper half of the data has $n_2 = 10$ values. The median of the upper half is the average of the 15th and 16th values. Counting: 1 (at 0)+4 (at 1)+7 (at 2) = 12, 12 + 3 (at 3) = 15, 12+4 (at 3)=16. So, $Q3 = 3$.
• Maximum: The largest value in the data set is 5.

Answer:

Minimum	Q1	Median	Q3	Maximum