If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

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Question: If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

Options:

Correct Answer: 7

Solution:

Q1 is the median of the first half of the data set {3, 7}, which is 7.

If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

If the data set {3, 7, 8, 12, 14} has a median of 8, what is the first quartile?

Step 1: Identify the data set, which is {3, 7, 8, 12, 14}.
Step 2: Confirm that the median of the data set is 8. The median is the middle number when the data is arranged in order.
Step 3: Split the data set into two halves. The first half is {3, 7} and the second half is {8, 12, 14}.
Step 4: Find the first quartile (Q1), which is the median of the first half of the data set.
Step 5: The first half of the data set is {3, 7}. Since there are two numbers, the median is the average of these two numbers.
Step 6: Calculate the average of 3 and 7: (3 + 7) / 2 = 5.
Step 7: Therefore, the first quartile (Q1) is 5.

Median – The median is the middle value of a data set when it is ordered from least to greatest.
Quartiles – Quartiles divide a data set into four equal parts, with Q1 being the median of the first half of the data.
Data Set Partitioning – Understanding how to split a data set into halves to find quartiles.