Question

the following refer to the following data set: 75.9 100.8 100.8 100.8 63.4 88 86.8 72.7 97 80.5 what is the arithmetic mean of this data set? mean = what is the median of this data set? median = what is the mode of this data set? mode =

Explanation:

Arithmetic Mean

Step1: Sum all data points

First, we add up all the values in the data set: \(75.9 + 100.8 + 100.8 + 100.8 + 63.4 + 88 + 86.8 + 72.7 + 97 + 80.5\)

Let's calculate step by step:
\(75.9 + 100.8 = 176.7\)
\(176.7 + 100.8 = 277.5\)
\(277.5 + 100.8 = 378.3\)
\(378.3 + 63.4 = 441.7\)
\(441.7 + 88 = 529.7\)
\(529.7 + 86.8 = 616.5\)
\(616.5 + 72.7 = 689.2\)
\(689.2 + 97 = 786.2\)
\(786.2 + 80.5 = 866.7\)

Step2: Divide by number of data points

There are 10 data points. So the mean is \(\frac{866.7}{10}\)

Step1: Order the data set

First, we sort the data in ascending order: \(63.4, 72.7, 75.9, 80.5, 86.8, 88, 97, 100.8, 100.8, 100.8\)

Step2: Find the middle value(s)

Since there are 10 (even number) data points, the median is the average of the 5th and 6th values.

The 5th value is \(86.8\) and the 6th value is \(88\).

Step3: Calculate the average

Median \(= \frac{86.8 + 88}{2}\)
\(= \frac{174.8}{2}\)
\(= 87.4\)

The mode is the value that appears most frequently in the data set. Looking at the data: \(100.8\) appears 3 times, which is more than any other value.

Answer:

The arithmetic mean is \(86.67\)

Median