Question

box plots
label and/or
calculate the 7 key
features
3, 6, 7, 9, 9, 11, 16, 18, 18, 19, 20, 22, 24
(number line from 0 to 25 with ticks at each integer)

Explanation:

Step1: Order the data

The data set is [3, 6, 7, 9, 9, 11, 16, 18, 18, 19, 20, 22, 24]. First, confirm it's ordered (already sorted here).

Step2: Find Minimum (Min)

The smallest value is $3$.

Step3: Find Maximum (Max)

The largest value is $24$.

Step4: Find Median (Q2)

There are $n = 13$ data points. The median is the $\frac{n + 1}{2}=7$th term. The 7th term is $16$.

Step5: Find Lower Quartile (Q1)

The lower half is [3, 6, 7, 9, 9, 11] (first 6 terms). The median of this half: $n = 6$, so median is the average of the 3rd and 4th terms. 3rd term: $7$, 4th term: $9$. $Q1=\frac{7 + 9}{2}=8$.

Step6: Find Upper Quartile (Q3)

The upper half is [18, 18, 19, 20, 22, 24] (last 6 terms). The median of this half: $n = 6$, average of 3rd and 4th terms. 3rd term: $19$, 4th term: $20$. $Q3=\frac{19 + 20}{2}=19.5$.

Step7: Find Interquartile Range (IQR)

$IQR = Q3 - Q1 = 19.5 - 8 = 11.5$.

Step8: Find Outlier Bounds

Lower bound: $Q1 - 1.5\times IQR = 8 - 1.5\times11.5 = 8 - 17.25 = -9.25$ (no lower outliers as data ≥ 3 > -9.25). Upper bound: $Q3 + 1.5\times IQR = 19.5 + 1.5\times11.5 = 19.5 + 17.25 = 36.75$ (no upper outliers as data ≤ 24 < 36.75).

The 7 key features for box - plot: Min = 3, Q1 = 8, Median (Q2)=16, Q3 = 19.5, Max = 24, IQR = 11.5, and no outliers.

Answer:

Min = 3, Q1 = 8, Median = 16, Q3 = 19.5, Max = 24, IQR = 11.5, No Outliers