consider the two data sets below:\ndata set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59\ndata set 2: 19, 25, 35…

consider the two data sets below:\ndata set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59\ndata set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99\n\nwhich of the following statements is true?\n\nthe values are not in order.\nthe data sets will have different values for their interquartile range.\nthe data sets will have the same values for their interquartile range.\nan outlier will have no effect on the range.

consider the two data sets below:\ndata set 1: 19, 25, 35, 38, 41, 49, 50, 52, 59\ndata set 2: 19, 25, 35, 38, 41, 49, 50, 52, 99\n\nwhich of the following statements is true?\n\nthe values are not in order.\nthe data sets will have different values for their interquartile range.\nthe data sets will have the same values for their interquartile range.\nan outlier will have no effect on the range.

Answer

Explanation:

Step1: Analyze Data Order

Check if data is ordered. Both sets: 19,25,35,38,41,49,50,52, (59 or 99). Values are in ascending order. So first option is false.

Step2: Recall Interquartile Range (IQR)

IQR = Q3 - Q1. Q1 is median of lower half, Q3 median of upper half (excluding median if odd n). For n=9, median is 5th term (41). Lower half: 19,25,35,38 (n=4, median Q1 = (25+35)/2 = 30). Upper half: 49,50,52, (59 or 99) (n=4, median Q3 = (50+52)/2 = 51).

Step3: Calculate IQR for Both Sets

For Data Set 1: IQR = 51 - 30 = 21. For Data Set 2: Upper half is 49,50,52,99. Q3 = (50+52)/2 = 51. So IQR = 51 - 30 = 21. IQR is same (outlier 99 doesn't affect Q1/Q3).

Step4: Analyze Range and Outlier

Range = Max - Min. Data Set 1: 59 -19 =40. Data Set 2:99 -19=80. Outlier (99) affects range, so fourth option false. Second option false (IQR same), third true.

Answer:

The data sets will have the same values for their interquartile range.