Answered

The stemplot below represents the number of bite-size snacks grabbed by 10 students in an activity for a statistics class.



Number of Snacks

$\begin{array}{l|lllll}

1 & 5 & 6 & 6 & 7 & 9 \\

2 & 0 & 1 & 3 & \\

3 & 2 & & & \\

4 & 2 & & &

\end{array}$



Key: 2|4 is a student who grabbed 24 snacks.



What is the correct set of data for the stemplot?


A$15, 16, 17, 19, 20, 21, 23, 32, 42$
B$15, 16, 16, 17, 19, 21, 23, 32, 42$
C$15, 16, 16, 17, 19, 20, 21, 23, 32, 42$
D$15, 15, 16, 17, 19, 20, 21, 23, 32, 42$

Verified Answer :

  • Read each stem as the tens digit and combine it with each leaf as the units digit to form the individual values.
  • Extract the numbers: \(15, 16, 16, 17, 19\) from the first row, \(20, 21, 23\) from the second, \(32\) from the third, and \(42\) from the fourth.
  • Combine these to form the complete data set: \(15, 16, 16, 17, 19, 20, 21, 23, 32, 42\).
  • The correct set is \(\boxed{15, 16, 16, 17, 19, 20, 21, 23, 32, 42}\).

Explanation

  1. Analyze the stemplot structure

To determine the set of data represented by a stemplot, we need to read each row, where the stem represents the tens digit and each leaf represents the unit's digit for a single data point. The stemplot is given as:

\[ \begin{array}{l|lllll} 1 & 5 & 6 & 6 & 7 & 9 \ 2 & 0 & 1 & 3 & & \ 3 & 2 & & & & \ 4 & 2 & & & & \end{array} \]

The key \(2 | 4\) indicates that the left digit (stem) is the tens place and the right digit (leaf) is the units place, so \(2 | 4\) means \(24\). We interpret each row according to this key.

  1. Extract the data points from each stem
  • For stem \(1\): The leaves are \(5, 6, 6, 7, 9\). Thus, the data points are \(15, 16, 16, 17, 19\).
  • For stem \(2\): The leaves are \(0, 1, 3\). Thus, the data points are \(20, 21, 23\).
  • For stem \(3\): The leaf is \(2\). Thus, the data point is \(32\).
  • For stem \(4\): The leaf is \(2\). Thus, the data point is \(42\).
  1. Aggregate and verify the data set

Combining all the extracted data points, we get the set:
\(15, 16, 16, 17, 19, 20, 21, 23, 32, 42\).

Counting the number of points:
\(1, 2, 3, 4, 5, 6, 7, 8, 9, 10\).
There are 10 students, so we have exactly 10 data points as expected. This set matches the third option provided in the question.

Examples

Stemplots are a great tool for quickly organizing and visualizing small datasets. For example, if you are tracking the scores of a math quiz for a class of students, you can use a stemplot to instantly see the distribution of grades, identifying where most scores fall and spotting any outliers, without needing to manually sort a long list of numbers. Understanding how to correctly read these plots ensures you can effectively analyze such data in real-time. For example, if you have scores like \(82, 85, 91, 93\), you can represent these with stem \(8\) having leaves \(2, 5\) and stem \(9\) having leaves \(1, 3\).

Related Questions