Question

The data show your strokes for 18 holes of miniature golf.Find the mean, median, ndmode(s) of the data. Which measure best represents the data? Explain your reasoning.4, 5, 3, 3, 1, 2, 3, 2, 4, 8, 2, 4, 4, 5, 2, 3, 6, 2

Answer 1

We have to calculate the mean, median and mode (or modes) of the data.

The size of the sample is n = 18.

We can start by sorting the data:

[1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 5, 5, 6, 8]

We can calculate the mean as:

`\begin{gathered} Mean=(1)/(n)\sum_{i\mathop{=}1}^nx_i \\ Mean=(1)/(18)(1+2*5+3*4+4*4+5*2+6+8) \\ Mean=(1)/(18)(1+10+12+16+10+6+8) \\ Mean=(1)/(18)(63) \\ Mean=3.5 \end{gathered}`

NOTE: we use the frequency of each value to save space, but we could have just add each value individually and get the same result.

We now will identify the median.

As we have an even sample size, the median will be the average between the 9th value and the 10th value.

Both values are 3, so the median is also 3.

The mode is the most frequent value in the dataset. In this case, the mode is 2, with a frequency of 5.

Both the mean and the median represent the data correctly as central measures. As the median is more robust than the mean, we can select the median as the best representation of the data.

Answer:

Mean = 3.5

Median = 3

Mode = 2

The median is a robust representation of the data.