What are the quartiles for the given dataset?
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
To find the quartiles for the given dataset, we first need to arrange the data in ascending order:
115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140
Now, we have 13 data points in total, so the median (Q2) is the middle value of the dataset, which is the 7th value since the dataset has an odd number of values: 127.
Next, we need to find the first quartile (Q1), which is the median of the lower half of the dataset. Since there are 6 values below the median (Q2), the 3rd value in the dataset is Q1: 122.
Similarly, we need to find the third quartile (Q3), which is the median of the upper half of the dataset. There are 6 values above the median (Q2), so the 11th value in the dataset is Q3: 136.
Therefore, the quartiles for the given dataset are:
Q1 = 122
Q2 = 127
Q3 = 136