Question

The third quartile and first quartile for the data 148,172,158,151,154,159,152,163,171,145

Answer 1

Answer:

How Quartiles Work

Just like the median divides the data into half so that 50% of the measurement lies below the median and 50% lies above it, the quartile breaks down the data into quarters so that 25% of the measurements are less than the lower quartile, 50% are less than the median, and 75% are less than the upper quartile.

First quartile: the lowest 25% of numbers

Second quartile: between 0% and 50% (up to the median)

Third quartile: 0% to 75%

Fourth quartile: the highest 25% of numbers.

Example of Quartile

Suppose the distribution of math scores in a class of 19 students in ascending order is:

59, 60, 65, 65, 68, 69, 70, 72, 75, 75, 76, 77, 81, 82, 84, 87, 90, 95, 98

First, mark down the median, Q2, which in this case is the 10th value: 75.Q1 is the central point between the smallest score and the median. In this case, Q1 falls between the first and fifth score: 68. (Note that the median can also be included when calculating Q1 or Q3 for an odd set of values. If we were to include the median on either side of the middle point, then Q1 will be the middle value between the first and 10th score, which is the average of the fifth and sixth score—(fifth + sixth)/2 = (68 + 69)/2 = 68.5).

Q3 is the middle value between Q2 and the highest score: 84. (Or if you include the median, Q3 = (82 + 84)/2 = 83).Now that we have our quartiles, let’s interpret their numbers. A score of 68 (Q1) represents the first quartile and is the 25th percentile. 68 is the median of the lower half of the score set in the available data—that is, the median of the scores from 59 to 75.

Q1 tells us that 25% of the scores are less than 68 and 75% of the class scores are greater. Q2 (the median) is the 50th percentile and shows that 50% of the scores are less than 75, and 50% of the scores are above 75. Finally, Q3, the 75th percentile, reveals that 25% of the scores are greater and 75% are less than 84.

Step-by-step explanation:

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Answer 2

Answer:

The first quartile is 151.5 and the third quartile is 167.

Explanation:

To find the first and third quartiles, we first need to arrange the data in order:

145, 148, 151, 152, 154, 158, 159, 163, 171, 172

The median is the middle value, which is (154 + 158) / 2 = 156.

To find the first quartile, we need to find the median of the lower half of the data:

145, 148, 151, 152, 154

The median of this data set is (151 + 152) / 2 = 151.5, which is the first quartile.

To find the third quartile, we need to find the median of the upper half of the data:

158, 159, 163, 171, 172

The median of this data set is (163 + 171) / 2 = 167, which is the third quartile.

Therefore, the first quartile is 151.5 and the third quartile is 167.

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