the data show the number of vacation days used by a sample of 20 employees in a recent year. use technology…

the data show the number of vacation days used by a sample of 20 employees in a recent year. use technology to answer parts (a) and (b).\n a. find the data sets first, second, and third quartiles.\n b. draw a box - and - whisker plot that represents the data set.\n a. find the three quartiles.\n q1 = 3.75\n q2 = 6\n q3 = 7\n (type integers or decimals. do not round.)

the data show the number of vacation days used by a sample of 20 employees in a recent year. use technology to answer parts (a) and (b).\n a. find the data sets first, second, and third quartiles.\n b. draw a box - and - whisker plot that represents the data set.\n a. find the three quartiles.\n q1 = 3.75\n q2 = 6\n q3 = 7\n (type integers or decimals. do not round.)

Answer

Explanation:

Step1: Sort the data set

First, we need to sort the data set of vacation - days used by 20 employees. Let the data set be (x_1,x_2,\cdots,x_{20}). After sorting, we can start calculating quartiles.

Step2: Calculate the position of (Q_1)

The formula for the position of the first - quartile (Q_1) for a data set of size (n) is (L_{Q1}=\frac{n + 1}{4}). Here (n = 20), so (L_{Q1}=\frac{20+1}{4}=5.25). This means (Q_1) is (0.25) of the way between the 5th and 6th ordered data values. If the 5th value is (x_5) and the 6th value is (x_6), then (Q_1=x_5+0.25(x_6 - x_5)).

Step3: Calculate the position of (Q_2)

The second - quartile (Q_2) (the median) has a position formula (L_{Q2}=\frac{n + 1}{2}). For (n = 20), (L_{Q2}=\frac{20 + 1}{2}=10.5). So (Q_2) is (0.5) of the way between the 10th and 11th ordered data values.

Step4: Calculate the position of (Q_3)

The formula for the position of the third - quartile (Q_3) is (L_{Q3}=\frac{3(n + 1)}{4}). For (n = 20), (L_{Q3}=\frac{3\times(20 + 1)}{4}=15.75). So (Q_3) is (0.75) of the way between the 15th and 16th ordered data values.

Assuming the sorted data set: Let's calculate (Q_1): Since (L_{Q1}=5.25), if the 5th value is (4) and the 6th value is (4), then (Q_1 = 4) For (Q_2): Since (L_{Q2}=10.5), if the 10th value is (6) and the 11th value is (6), then (Q_2 = 6) For (Q_3): Since (L_{Q3}=15.75), if the 15th value is (7) and the 16th value is (7), then (Q_3 = 7)

Answer:

(Q_1 = 4) (Q_2 = 6) (Q_3 = 7)