Joanna set a goal to drink more water daily. The number of ounces of water she drank each of the last seven days is shown below.
60, 58, 64, 64, 68, 50, 57. On the eighth day, she drinks 82 ounces of water. Select all the true statements about the effect of the eighth day's amount on Joanna's daily amount distribution. The average daily amount of water is the same with or without the inclusion of the eighth day's amount. The median amount of water is the same with or without the inclusion of the eighth day's amount. The interquartile range of the data decreases when the eighth day's amount is included in the data. The interquartile range of the data increases when the eighth day's amount is included in the data. The median amount of water is higher when the eighth day's amount is included in the data.
(a) Data with the eight day's measurement. Raw data: [60,58,64,64,68,50,57,82], Sorted data: [50,57,58,60,64,64,68,82] Sample size = 8 (even) mean = 62.875 median = (60+64)/2 = 62 1st quartile = (57+58)/2 = 57.5 3rd quartile = (64+68)/2 = 66 IQR = 66 - 57.5 = 8.5
(b) Data without the eight day's measurement. Raw data: [60,58,64,64,68,50,57] Sorted data: [50,57,58,60,64,64,68] Sample size = 7 (odd) mean = 60.143 median = 60 1st quartile = 57 3rd quartile = 64 IQR = 64 -57 = 7
Answers: 1. The average is the same with or without the 8th day's data. FALSE 2. The median is the same with or without the 8th day's data. FALSE 3. The IQR decreases when the 8th day is included. FALSE 4. The IQR increases when the 8th day is included. TRUE 5. The median is higher when the 8th day is included. TRUE
Using 1/2 as a benchmark, 1/5 is the only one less than 1/2. That is the least. You can turn 2/3 and 5/8 into fractions with common denominators. 2/3=16/24 and 5/8= 15/24. 5/8 is less than 2/3, therefore resulting in the answer.
