Question

Find the median and first and third quartile for the following data:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22​

Answer 1

Given: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22​ $(n=11)$

To find: Median, First quartile, and Third quartile

Step-by-step explanation:

• Median: The median is the value that divides a data sample, a population, or a probability distribution into the upper and lower halves.

• Because there are 11 numbers in this sequence, we'll choose the sixth number and skip averaging the two middle numbers.  

Hence, the answer would be 12.

• First Quartile: When data points are presented in ascending order, the lower quartile, or first quartile (Q1), is the value under which $25\%$ data points are located.

Formula: $\frac{(n+1)}{4^{th} }$ term

∴ $\frac{11+1}{4}$

∴ $\frac{12}{4}=3$

Hence, the third term from the series is 6 so the first quartile would be 6.

Third Quartile: When data points are presented in ascending order, the upper quartile, or third quartile (Q3), is the value under which 75 percent of data points are located.

Formula: $\frac{3(n+1) }{4^{th} }$ term

∴ $3\times3=9$ (since we've already calculated the value of $\frac{n+1}{4^{th} }$ term)

Hence, the ninth term from the series is 18 so the first quartile would be 18.