Question

find the mean, median, and mode of the data set.
number of books read
sylvester 218 edmund 224
rashin 217 treya 217
mean: 217.5; median: 219; mode: 217
mean: 219; median: 217; mode: 217.5
mean: 219; median: 217.5; mode: 217
mean: 217.5; median: 217; mode: 219

Explanation:

Step1: Calculate the mean

The mean is the sum of all values divided by the number of values.
The data set is \(217,217,218,224\).
The sum is \(217 + 217+218 + 224=876\).
The number of values \(n = 4\).
The mean \(\bar{x}=\frac{876}{4}=219\).

Step2: Calculate the median

For a data set with \(n = 4\) (even number of values), the median is the average of the \(\frac{n}{2}\) - th and \((\frac{n}{2}+1)\) - th ordered values.
Order the data: \(217,217,218,224\).
\(\frac{n}{2}=2\), \(\frac{n}{2}+1 = 3\).
The median \(M=\frac{217 + 218}{2}=\frac{435}{2}=217.5\).

Step3: Calculate the mode

The mode is the value that appears most frequently in the data set.
In the data set \(217,217,218,224\), the value \(217\) appears twice and \(218\) and \(224\) appear once. So the mode is \(217\).

Answer:

Mean: \(219\); Median: \(217.5\); Mode: \(217\) (corresponding to the third option)