Question

the stemplot below represents the number of bite - size snacks grabbed by 37 students in an activity for a statistics class. which of the following statements best describes the distribution? number of snacks the distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 15 to 45. there are no outliers. the distribution of the number of snacks grabbed is symmetric with a center around 18 and varies from 12 to 45. there are possible outliers at 38, 42, and 45. the distribution of the number of snacks grabbed is skewed left with a center around 18 and varies from 12 to 45. there are possible outliers at 38, 42, and 45. the distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. there are possible outliers at 38, 42, and 45. key: 2|4 is a student who grabbed 24 snacks.

Explanation:

Step1: Analyze the shape of the distribution

In a stemplot, if the tail of the distribution is longer on the right - hand side, it is skewed right. Here, most of the data is concentrated on the left (lower values) and there are a few larger values on the right. So the distribution is skewed right.

Step2: Determine the center

The center (a measure like the median or the approximate middle of the data) can be estimated. Looking at the stemplot, the middle - most values (since \(n = 37\), the \(19^{th}\) value) is around 18.

Step3: Check the range and outliers

The minimum value is 12 (from the first stem - and - leaf row: 1|2) and the maximum is 45 (from the last stem - and - leaf row: 4|5). Using the inter - quartile range rule for outliers (\(Q_1-1.5\times IQR\) and \(Q_3 + 1.5\times IQR\)), we first find \(Q_1\), \(Q_3\).
The first half of the data (first 18 values) has \(Q_1\approx15\) and the second half (last 18 values) has \(Q_3\approx25\), \(IQR=Q_3 - Q_1=25 - 15 = 10\). \(Q_3+1.5\times IQR=25+15 = 40\). Values 42 and 45 are greater than 40, so they are possible outliers.

Answer:

The distribution of the number of snacks grabbed is skewed right with a center around 18 and varies from 12 to 45. There are possible outliers at 38, 42, and 45.