Question

What are the quartiles for the given dataset? 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140 (1 point) Responses Q1 Q 1 : 121; Q2 Q 2 : 127; Q3 Q 3 : 134 upper Q subscript 1 baseline : 121; upper Q subscript 2 baseline : 127; upper Q subscript 3 : 134 Q1 Q 1 : 115; Q2 Q 2 : 127; Q3 Q 3 : 140 upper Q subscript 1 baseline : 115; upper Q subscript 2 baseline : 127; upper Q subscript 3 : 140 Q1 Q 1 : 122; Q2 Q 2 : 127.5; Q3 Q 3 : 132 upper Q subscript 1 baseline : 122; upper Q subscript 2 baseline : 127.5; upper Q subscript 3 : 132 Q1 Q 1 : 121; Q2 Q 2 : 127.5; Q3 Q 3 : 134

Answer 1

To calculate the quartiles for the given dataset, we first need to sort the dataset (though it is already sorted in this case):

The dataset: 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140

1. Finding Q2 (Median):

   • The number of data points (n) is 13, which is odd.
   • Q2 (the median) is the middle value:
   • Median = 7th value = 127.

2. Finding Q1:

   • Q1 is the median of the first half of the data (the lower 6 values):
     • Lower half: 115, 117, 120, 122, 125, 125
     • Q1 = Median of (115, 117, 120, 122, 125, 125) = (120 + 122) / 2 = 121.

3. Finding Q3:

   • Q3 is the median of the second half of the data (the upper 6 values):
     • Upper half: 128, 131, 132, 136, 136, 140
     • Q3 = Median of (128, 131, 132, 136, 136, 140) = (132 + 136) / 2 = 134.

Therefore, the quartiles for the dataset are:

• Q1 = 121
• Q2 = 127
• Q3 = 134

Thus, the correct response is: Q1: 121; Q2: 127; Q3: 134