find the median, first quartile (q1) and the third quartile (q3) for the data shown, which is already…

Explanation:

Step1: Find the median

For a data - set with $n = 10$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+ 1)$th ordered values. Here, $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$. The 5th value is $15.4$ and the 6th value is $16$. So, the median $M=\frac{15.4 + 16}{2}=15.7$.

Step2: Find the first quartile (Q1)

The first quartile is the median of the lower half of the data. The lower half of the data consists of the first 5 values: $2,4.1,6.6,14.4,15.4$. Since $n_1 = 5$ (an odd - number of data points), the median of this lower - half (Q1) is the $\frac{5 + 1}{2}=3$rd value. So, $Q1=6.6$.

Step3: Find the third quartile (Q3)

The third quartile is the median of the upper half of the data. The upper half of the data consists of the last 5 values: $16,16.5,19.2,24.7,26.6$. Since $n_2 = 5$ (an odd - number of data points), the median of this upper - half (Q3) is the $\frac{5+1}{2}=3$rd value. So, $Q3 = 19.2$.

Answer:

Median = $15.7$ $Q1=6.6$ $Q3 = 19.2$