Question

the life spans, in years, of some plants in a nursery are shown below:
5, 3.2, 4.1, 3.8, 3.1, 3.2, 5.8, 3.8, 4.2, 4.3
jack made the following box plot to represent the life spans:

which of the following did jack incorrectly show on his box plot?
median
minimum
first quartile
third quartile

Explanation:

Step1: Sort the data set

Sorted data: $3.1, 3.2, 3.2, 3.8, 3.8, 4.1, 4.2, 4.3, 5, 5.8$

Step2: Find minimum value

Minimum = smallest value: $3.1$

Step3: Calculate median (Q2)

For $n=10$ (even), median = $\frac{5^{th}+6^{th}}{2} = \frac{3.8+4.1}{2} = 3.95$

Step4: Calculate first quartile (Q1)

Q1 = median of lower half: $\frac{3.2+3.2}{2} = 3.2$

Step5: Calculate third quartile (Q3)

Q3 = median of upper half: $\frac{4.3+5}{2} = 4.65$

Step6: Find maximum value

Maximum = largest value: $5.8$

Step7: Compare to box plot

Jack's box plot shows max ≈5.8, min≈3.1, Q1≈3.2, Q3≈4.2, median≈4. Q3 is incorrectly plotted as ~4.2 instead of 4.65.

Answer:

Third quartile