Question

find each measure of central tendency. type exact values. do not round. mean: 4.25 median: 2 mode: 1 based on the shape of the distribution, which measure of central tendency would be best to describe the typical number of winter olympic gold - medal wins by a top 20 medal - winning country in 2010. choose your answer... 2010 winter olympics gold medal wins by top 20 medal - winning countries number of gold medals won

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