Find the five-number summary for the data.
{232, 198, 214, 205, 222, 228, 208, 237, 217, 199, 213, 208, 228, 224, 203}
To find the five-number summary for the given data, we need to calculate the following statistics:
1. Minimum: the smallest value in the dataset.
2. Q1 (first quartile): the median of the lower half of the data, which is the median of the data excluding the median itself and all values greater than it.
3. Median: the middle value of the dataset when arranged in ascending order.
4. Q3 (third quartile): the median of the upper half of the data, which is the median of the data excluding the median itself and all values smaller than it.
5. Maximum: the largest value in the dataset.
First, let's sort the data in ascending order:
{198, 199, 203, 205, 208, 208, 213, 214, 217, 222, 224, 228, 228, 232, 237}
1. The minimum value is 198.
2. Q1: Since there are 15 values in the dataset, the median of the lower half will be the 8th value. So, Q1 = 213.
3. Median: Since there are 15 values, the median will be the 8th value as well. So, the median = 214.
4. Q3: Similarly, Q3 will be the median of the upper half, which is the 8th value from the end. So, Q3 = 228.
5. The maximum value is 237.
Therefore, the five-number summary for the given dataset is:
Minimum: 198
Q1: 213
Median: 214
Q3: 228
Maximum: 237