Question

1. based on the dot plot below, list all of the values in the data set 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: List data - set values

Count the number of dots for each value on the x - axis. There is 1 dot above 0, 3 dots above 1, 5 dots above 2, 3 dots above 3, 3 dots above 4, and 1 dot above 5. The data - set is: 0, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 4, 4, 4, 5.

Step2: Calculate the mode

The mode is the most frequently occurring value. Here, the value 2 appears 5 times, more frequently than any other value, so the mode is 2.

Step3: Calculate the median

There are 16 data points. The median for a data - set with \(n = 16\) (an even number of data points) is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values. The 8th and 9th ordered values are both 2, so the median is \(\frac{2 + 2}{2}=2\).

Step4: Calculate the mean

The mean \(\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}\). \(\sum_{i = 1}^{16}x_{i}=0\times1 + 1\times3+2\times5 + 3\times3+4\times3+5\times1=0 + 3+10 + 9+12 + 5=39\), and \(n = 16\). So the mean \(\bar{x}=\frac{39}{16}=2.4375\).

Answer:

(2) The median and the mode are the same.