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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
: 115; Q2
: 127; Q3
: 140
upper Q subscript 1 baseline : 115; upper Q subscript 2 baseline : 127; upper Q subscript 3 : 140

Q1
: 121; Q2
: 127; Q3
: 134
upper Q subscript 1 baseline : 121; upper Q subscript 2 baseline : 127; upper Q subscript 3 : 134

Q1
: 121; Q2
: 127.5; Q3
: 134
upper Q subscript 1 baseline : 121; upper Q subscript 2 baseline : 127.5; upper Q subscript 3 : 134

Q1
: 122; Q2
: 127.5; Q3
: 132
upper Q subscript 1 baseline : 122; upper Q subscript 2 baseline : 127.5; upper Q subscript 3 : 132

1 answer

To find the quartiles for the given dataset, we first need to sort the data (though it's already sorted) and then follow these steps:

  1. Find Q2 (Median):

    • The dataset has 13 numbers (an odd count), so Q2 is the middle number.
    • Q2 = 7th number = 127

  2. Find Q1:

    • Q1 is the median of the first half of the dataset (the first 6 numbers).
    • First half: 115, 117, 120, 122, 125, 125
    • The median of these 6 numbers is the average of the 3rd (120) and 4th (122) values.
    • Q1 = (120 + 122) / 2 = 121

  3. Find Q3:

    • Q3 is the median of the second half of the dataset (the last 6 numbers).
    • Second half: 128, 131, 132, 136, 136, 140
    • The median of these 6 numbers is the average of the 3rd (132) and 4th (136) values.
    • Q3 = (132 + 136) / 2 = 134

Thus, the quartiles for the dataset are:

  • Q1: 121
  • Q2: 127
  • Q3: 134

Therefore, the correct option is:

Q1: 121; Q2: 127; Q3: 134