question #2\nfind the lower quartile for the following set of data:\n11 12 13 17 17\n17 18 21 22\nsaved…

Explanation:

Step1: Arrange data in ascending order

The data set for question #2 is already in ascending - order: (11,12,13,17,17,17,18,21,22). The number of data points (n = 9).

Step2: Calculate the position of the lower - quartile

The formula for the position of the lower - quartile (Q_1) when (n) is odd is (Q_1=\left(\frac{n + 1}{4}\right))th value. Substituting (n = 9) into the formula, we get (\frac{9+1}{4}=2.5)th value.

Step3: Find the lower - quartile

The (2.5)th value is the average of the 2nd and 3rd ordered values. The 2nd value is (12) and the 3rd value is (13). So, (Q_1=\frac{12 + 13}{2}=12.5).

For question #3:

Step1: Arrange data in ascending order

The data set is (42,43,43,44,45,47,47,48,48,51,52,52,52,52,54,55,55). Here (n = 17).

Step2: Calculate the position of (Q_1) and (Q_3)

The position of (Q_1=\left(\frac{n + 1}{4}\right))th value. Substituting (n = 17), we get (\frac{17+1}{4}=4.5)th value. The (4.5)th value is the average of the 4th and 5th ordered values. The 4th value is (44) and the 5th value is (45), so (Q_1=\frac{44 + 45}{2}=44.5). The position of (Q_3=\left(\frac{3(n + 1)}{4}\right))th value. Substituting (n = 17), we get (\frac{3\times(17 + 1)}{4}=13.5)th value. The (13.5)th value is the average of the 13th and 14th ordered values. The 13th value is (52) and the 14th value is (52), so (Q_3 = 52).

Step3: Calculate the inter - quartile range (IQR)

The formula for (IQR=Q_3−Q_1). Substituting (Q_1 = 44.5) and (Q_3 = 52), we get (IQR=52-44.5 = 7.5).

Answer:

Question #2: (12.5) Question #3: (7.5)