Question

the heights, in cm, of some plants in a greenhouse are shown below. 13.5, 12.2, 12.8, 12.8, 12.3, 12, 13.9, 14, 14.2, 12.6 jack made the following box plot to represent the heights. which of the following did jack incorrectly show on his box plot? median minimum first quartile third quartile

Explanation:

Step1: Sort the height data

Sorted data: $12, 12.2, 12.3, 12.6, 12.8, 12.8, 13.5, 13.9, 14, 14.2$

Step2: Find minimum value

Minimum = smallest value = $12$

Step3: Calculate median (Q2)

For $n=10$, median = $\frac{5^{th}+6^{th}}{2} = \frac{12.8+12.8}{2} = 12.8$

Step4: Calculate first quartile (Q1)

Lower half: $12, 12.2, 12.3, 12.6, 12.8$
Q1 = median of lower half = $12.3$

Step5: Calculate third quartile (Q3)

Upper half: $12.8, 13.5, 13.9, 14, 14.2$
Q3 = median of upper half = $13.9$

Step6: Compare to box plot

Box plot shows: Min=$12$, Q1=$12.2$, Median=$12.8$, Q3=$13.9$, Max=$14.2$. The incorrect value is Q1.

Answer:

First quartile