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

Q1
: 115; Q2
: 127; Q3
: 140
upper Q subscript 1 baseline : 115; upper Q subscript 2 baseline : 127; upper Q subscript 3 : 140

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

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

1 answer

To calculate the quartiles (Q1, Q2, and Q3) for the dataset:

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

Step 1: Sort the data (already sorted) The data is already sorted in ascending order.

Step 2: Calculate Q2 (Median) The median (Q2) is found by taking the middle number of the dataset. Since there are 13 numbers (odd count), the median is the 7th number:

Q2 = 127 (the middle number)

Step 3: Calculate Q1 (First Quartile) Q1 is the median of the first half of the dataset (the first 6 numbers):

First half: 115, 117, 120, 122, 125, 125

Median of first half (Q1) = (120 + 122) / 2 = 121

Step 4: Calculate Q3 (Third Quartile) Q3 is the median of the second half of the dataset (the last 6 numbers):

Second half: 128, 131, 132, 136, 136, 140

Median of second half (Q3) = (132 + 136) / 2 = 134

Therefore, the quartiles are:

  • Q1 = 121
  • Q2 = 127
  • Q3 = 134

The correct response is: Q1: 121; Q2: 127; Q3: 134