Question

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.

Answer 1

(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