find each measure of central tendency. type exact values. do not round. mean: 4.25 median: 2 mode: 1 based…

Explanation:

Step1: Count data - point frequency

Count the number of 'x's for each value on the number - line.

Step2: Calculate the mode

The mode is the value that appears most frequently. By counting, the value 1 appears 4 times, which is the most frequent. So the mode is 1.

Step3: Calculate the median

First, find the total number of data points. Counting all the 'x's, there are 20 data points. Since (n = 20) (an even number), the median is the average of the (\frac{n}{2})th and ((\frac{n}{2}+ 1))th ordered data points. Ordering the data (by the number of gold - medals values), the 10th and 11th ordered data points are both 2. So the median is (\frac{2 + 2}{2}=2).

Step4: Calculate the mean

The mean (\bar{x}=\frac{\sum_{i = 1}^{k}x_{i}f_{i}}{n}), where (x_{i}) is the value and (f_{i}) is its frequency and (n) is the total number of data points. [ \begin{align*} \sum_{i = 1}^{k}x_{i}f_{i}&=0\times2 + 1\times4+2\times3 + 3\times1+4\times2+5\times2+6\times2+9\times2+10\times1+14\times1\ &=0 + 4+6 + 3+8+10+12+18+10+14\ &=85 \end{align*} ] Since (n = 20), the mean (\bar{x}=\frac{85}{20}=4.25)

Answer:

Mode: 1 Median: 2 Mean: 4.25