Tthe quartiles for the given data set are:
Q1: 120, Q2: 200 (median), Q3: 260, Q4: 600
Finding the quartiles involves dividing the data set into four equal parts.
1. Arrange the data in ascending order: 50, 100, 120, 125, 125, 155, 200, 200, 220, 250, 260, 300, 310, 320, 600.
2. Calculate the number of data points: Having 15 values, the number of data points (n) is 15.
3. Calculate the positions of the quartiles:
First quartile (Q1): Divide (n) by 4.
Q1 = (15 / 4) = 3.75.
Having whole numbers in this situation, take the third smallest value, which is 120.
Second quartile (Q2): The median, which is the middle value when the data is sorted.
Q2 = the 8th value, which is 200.
Third quartile (Q3): Divide (3n) by 4.
Q3 = (3 × 15) / 4 = 45 / 4 = 11.25.
Take the third smallest value from the second half of the sorted data, which is 260.
Fourth quartile (Q4): Q4 is represented by the largest value in the data set (i.e Q4 = 600).
Therefore, the quartiles for the given data set are:
Q1: 120
Q2: 200 (median)
Q3: 260
Q4: 600