a sample of 10 boxes of skittles has these weights in grams: 25, 28, 29, 30, 34, 35, 35, 37, 38. which of…

a sample of 10 boxes of skittles has these weights in grams: 25, 28, 29, 30, 34, 35, 35, 37, 38. which of the following box - and - whiskers plots best represents the data?

a sample of 10 boxes of skittles has these weights in grams: 25, 28, 29, 30, 34, 35, 35, 37, 38. which of the following box - and - whiskers plots best represents the data?

Answer

Answer:

To determine the correct box - and - whiskers plot, we need to find the five - number summary (minimum, first quartile $Q_1$, median, third quartile $Q_3$, maximum) of the data set.

  1. First, order the data set: $25,28,29,30,34,35,35,37,38$.
    • The minimum value is $25$.
    • The maximum value is $38$.
  2. Calculate the median ($Q_2$):
    • Since $n = 10$ (an even number of data points), the median is the average of the $\frac{n}{2}$th and $(\frac{n}{2}+1)$th ordered data points.
    • $\frac{n}{2}=5$ and $\frac{n}{2}+1 = 6$.
    • The median $Q_2=\frac{34 + 35}{2}=34.5$.
  3. Calculate the first quartile ($Q_1$):
    • The lower half of the data is $25,28,29,30,34$. Since $n_1 = 5$ (an odd number of data points), the first quartile $Q_1$ is the middle value of the lower - half data set, so $Q_1 = 29$.
  4. Calculate the third quartile ($Q_3$):
    • The upper half of the data is $35,35,37,38$. Since $n_2 = 4$ (an even number of data points), $Q_3=\frac{35+37}{2}=36$.

In a box - and - whiskers plot:

  • The left - hand side of the box is at $Q_1 = 29$.
  • The line inside the box is at the median $Q_2 = 34.5$.
  • The right - hand side of the box is at $Q_3 = 36$.
  • The left whisker extends to the minimum value $25$.
  • The right whisker extends to the maximum value $38$.

We need to visually inspect the given box - and - whiskers plots to find the one that matches these values. Without the actual options labeled, we can't give a specific choice, but the correct plot should have a box starting at approximately $29$, a line in the box at $34.5$, a box ending at $36$, and whiskers extending to $25$ and $38$.

Explanation:

Step1: Order the data

$25,28,29,30,34,35,35,37,38$

Step2: Find the minimum and maximum

Minimum = $25$, Maximum = $38$

Step3: Calculate the median

$Q_2=\frac{34 + 35}{2}=34.5$

Step4: Find the lower half and $Q_1$

Lower half: $25,28,29,30,34$, $Q_1 = 29$

Step5: Find the upper half and $Q_3$

Upper half: $35,35,37,38$, $Q_3=\frac{35 + 37}{2}=36$