Question

If there are 21 values in a data set in order from smallest to largest, what is the first quartile of the data set?

A. The mean of the 6th and 7th values
B. The mean of the 5th and 6th values
C. The mean of the 3rd and 4th values
D. The mean of the 4th and 5th values

Answer 1

I think the answer is B) The mean of the 5th and 6th values

Answer 2

Answer with explanation:

Total Number of Variate in the Data set = 21

Since number of Variate is odd, median is given by the formula:

     $=\frac{\text{Total number of terms}+1}{2}\\\\=\frac{21+1}{2}\\\\=11^{\text{th term}}$

$Q_{1}$

      = Mid value between  lowest Variate and Median value.

→→Mid value of first 11 Terms is given by

     $=\frac{\text{Total number of terms}+1}{2}\\\\=\frac{11+1}{2}\\\\=6^{\text{th term}}$

Most Appropriate Option:⇒

Option A: →The mean of the 6th and 7th values