Question

find the median of the data. 75, 78, 80, 82, 82, 91, 96, 100 mean median mode sum (add) all data number of data middle number when all data is in order from least to greatest most appears a lot of times a 82 b 85.5 c 82.5

Explanation:

Step1: Determine the number of data points

The data set is \(75,78,80,82,82,91,96,100\). The number of data points \(n = 8\) (an even number).

Step2: Use the formula for median of an even - numbered data set

For a data set with \(n\) (even) data points, the median is the average of the \(\frac{n}{2}\)th and \((\frac{n}{2}+ 1)\)th ordered values.
Here, \(\frac{n}{2}=\frac{8}{2}=4\) and \(\frac{n}{2}+1 = 5\).
The 4th value is \(82\) and the 5th value is \(82\).

Step3: Calculate the median

Median \(M=\frac{82 + 82}{2}=\frac{164}{2}=82\)

Answer:

A. 82