Question

for exercises 1 and 2, answer the questions. 1. the number of plastic recyclables collected during the week by each 6th-grade class was 62, 51, 58, 53, 55, 61, 52, 64, 60, and 61. what is the median number of plastic recyclables collected? what is the mode?

Explanation:

Step1: Order the data

First, we need to order the given data set from smallest to largest. The data set is \( 62, 51, 58, 53, 55, 61, 52, 64, 60, 61 \). After ordering, we get: \( 51, 52, 53, 55, 58, 60, 61, 61, 62, 64 \).

Step2: Find the median

The median is the middle value of a data set when it is ordered. Since there are \( n = 10 \) (an even number) values, the median is the average of the \( \frac{n}{2} \)-th and \( (\frac{n}{2}+1) \)-th values.
\( \frac{n}{2}=\frac{10}{2} = 5 \)-th value and \( \frac{n}{2}+1=6 \)-th value.
The 5th value is \( 58 \) and the 6th value is \( 60 \).
The median is \( \frac{58 + 60}{2}=\frac{118}{2}=59 \).

Step3: Find the mode

The mode is the value that appears most frequently in the data set. Looking at the ordered data \( 51, 52, 53, 55, 58, 60, 61, 61, 62, 64 \), we can see that \( 61 \) appears twice and all other values appear only once. So the mode is \( 61 \).

Answer:

Median: \( 59 \), Mode: \( 61 \)