Question

Cholesterol levels, in mg/dl, for a random sample of 38 adults are listed below. Find the first, second, and third quartiles.

101 124 128 132 135 139 141 145 148 151
155 156 162 165 169 170 171 173 175 177
178 180 181 184 185 188 189 190 194 197
199 200 201 205 210 214 217 220

Provide your answer below:
Q1 =
Q2 =
Q3 =

Answer 1

The quartiles of cholesterol levels for a sample of 38 adults are Q1 = 151, Q2 = 170.5, and Q3 = 197.

Step-by-step explanation:

To find the first (Q1), second (Q2), and third (Q3) quartiles of the given cholesterol levels of the 38 adults, we first need to arrange the data in ascending order, which has already been done in the question.

Since there are 38 data points, to find Q1, which is the median of the first half of the data, we find the median of the first 19 numbers.

Because 19 is an odd number, Q1 will be the 10th value in the list. Similarly, Q2, which is the median of the entire dataset, will be the average of the 19th and 20th values because we have an even number of data points. For Q3, we find the median of the last 19 numbers, which will again be the 10th value of that second half of the data set.

Let's calculate these one by one:

1. Q1 (First Quartile): The 10th value in the ordered list is 151.
2. Q2 (Second Quartile or Median): The average of the 19th and 20th values (170 and 171) is (170 + 171) / 2 = 170.5
3. Q3 (Third Quartile): The 10th value from the end or the 29th value in the ordered list is 197.

Therefore, the quartiles are:

• Q1 = 151
• Q2 = 170.5
• Q3 = 197