Question

using the following stem & leaf plot, find the five number summary for the data. view in full window so that you have 6 rows of data.
1|0 2
2|3 4 4 5 9
3|
4|2 2 7 9
5|0 4 5 6 8 9
6|0 8
min =
q1 =
med =
q3 =
max =
question help: video 1 video 2 message instructor

Explanation:

Step1: List all data values

The data values from the stem - and - leaf plot are: 10, 12, 23, 24, 24, 25, 29, 30, 42, 42, 47, 49, 50, 54, 55, 56, 58, 59, 60, 68.

Step2: Find the minimum

The minimum value is the smallest number in the data set. So, Min = 10.

Step3: Find the first quartile ($Q_1$)

First, order the data. There are $n = 20$ data points. The position of $Q_1$ is $\frac{n + 1}{4}=\frac{20+ 1}{4}=5.25$. The 5th value is 24 and the 6th value is 25. So, $Q_1=24+(25 - 24)\times0.25 = 24.25$.

Step4: Find the median (Med)

The position of the median for $n = 20$ (an even - numbered data set) is between the $\frac{n}{2}=10$th and $\frac{n}{2}+1 = 11$th ordered values. The 10th value is 42 and the 11th value is 47. So, Med=$\frac{42 + 47}{2}=44.5$.

Step5: Find the third quartile ($Q_3$)

The position of $Q_3$ is $\frac{3(n + 1)}{4}=\frac{3\times(20 + 1)}{4}=15.75$. The 15th value is 55 and the 16th value is 56. So, $Q_3=55+(56 - 55)\times0.75 = 55.75$.

Step6: Find the maximum

The maximum value is the largest number in the data set. So, Max = 68.

Answer:

Min = 10
$Q_1$ = 24.25
Med = 44.5
$Q_3$ = 55.75
Max = 68