Question

What are the quartiles for the given data set 115, 117, 120, 122, 125, 125, 127, 128, 131, 132, 136, 136, 140,

Answer 1

To find the quartiles for this data set, first arrange the data in ascending order:

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

There are 13 values in the data set, so the middle value is the 7th value:

Q2 (median): (125 + 125)/2 = 125

To find Q1 and Q3, split the data set into two halves at the median (125):

Lower half: 115, 117, 120, 122, 125
Upper half: 127, 128, 131, 132, 136, 136, 140

For Q1 (1st quartile), find the median of the lower half:

Q1: (117 + 120)/2 = 118.5

For Q3 (3rd quartile), find the median of the upper half:

Q3: (131 + 132)/2 = 131.5

Therefore, the quartiles for the given data set are:
Q1 = 118.5
Q2 = 125
Q3 = 131.5