Question

using the given data, find the following. 5 24 20 18 21 11 send data to excel part: 0 / 2 part 1 of 2 identify the five - number summary. round your answers to one decimal place as needed. low =, q1 =, md =, q3 =, high =

Explanation:

Step1: Sort the data

$5, 11, 18, 20, 21, 24$

Step2: Find the low value

The lowest number in the sorted - data is $5$. So, Low = $5$.

Step3: Find the high value

The highest number in the sorted - data is $24$. So, High = $24$.

Step4: Find the median (MD)

Since there are $n = 6$ data points, the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered values. $\frac{6}{2}=3$ and $\frac{6}{2}+1 = 4$. The 3rd and 4th values are $18$ and $20$. So, $MD=\frac{18 + 20}{2}=19$.

Step5: Find the first quartile ($Q_1$)

The lower half of the data is $5, 11, 18$. Since there are $n = 3$ data points in the lower half, the first quartile is the middle value of the lower - half. So, $Q_1 = 11$.

Step6: Find the third quartile ($Q_3$)

The upper half of the data is $20, 21, 24$. Since there are $n = 3$ data points in the upper half, the third quartile is the middle value of the upper - half. So, $Q_3 = 21$.

Answer:

Low = $5$, $Q_1 = 11$, $MD = 19$, $Q_3 = 21$, High = $24$