Question

Find the 5 number summary for the data shown below.1848815814259130485 number summary:Check Answer

Answer 1

isLet's start finding the 5 number summary of the given data by arranging them first from the lowest value to the highest value. We have

$\rightarrow4,5,15,18,30,42,48,81,88,91$

Based on this arrangement, we can find two important numbers for the 5 number summary which are the minimum and the maximum numbers. The minimum number is 4 while the maximum number is 91.

The next number for the 5 number summary is the median of the data. The median can be computed as the average of the data. We have

$\mu=\frac{4+5+15+18+30+42+48+81+88+91}{10}=42.2$

For the final two numbers for the 5 number summary, let's arrange the data set where we have the lower part (numbers below the median) and the upper part (number above the median). We have

$\begin{gathered} \rightarrow4,5,15,18,30 \\ \rightarrow48,81,88,91 \end{gathered}$

For the lower part data set, the middle number represents its median. Hence, the median for the lower part is 15. For the upper limit, since we don't have a middle term, let's compute for the median. We have

$\frac{48+81+88+91}{4}=77$

The closest number to 77 on the number set is 81, hence, 81 is the other number for the 5 number summary.

Therefore, the 5 number summary for the data given is 4, 15, 42.2, 81, and 91.