Question

1. a class of 20 students was surveyed to determine the number of pets each student owned. the data are represented in the dot - plot below. which statement about the data is correct? 1) the mean and the median are the same. 2) the median and the mode are the same. 3) the mean and the mode are the same. 4) the mean, median, and mode are all the same.

Explanation:

Step1: Calculate the mean

First, find the sum of all data - points and divide by the number of data - points. There is 1 student with 0 pets, 4 students with 1 pet, 6 students with 2 pets, 4 students with 3 pets, 3 students with 4 pets, and 2 students with 5 pets. The sum is \(0\times1 + 1\times4+2\times6 + 3\times4+4\times3+5\times2=0 + 4+12 + 12+12+10 = 50\). The number of students \(n = 20\). The mean \(\bar{x}=\frac{50}{20}=2.5\).

Step2: Calculate the median

Since \(n = 20\) (an even - numbered data set), the median is the average of the 10th and 11th ordered data - points. Counting the data points: \(1\) (for \(0\) pets) \(+4\) (for \(1\) pet) \(+6\) (for \(2\) pets) \(=11\). The 10th and 11th ordered data - points are both 2. So the median \(M = 2\).

Step3: Calculate the mode

The mode is the value that appears most frequently. The number of pets with the highest frequency is 2 (it appears 6 times). So the mode \(Mo = 2\).

Answer:

1. The median and the mode are the same.