Question

interpreting the shape of the data
enter two or more numbers in the table to create a histogram.
enter the data to create a histogram. then check all that apply.
runs 1 7 1 6 1 2 8 6 8 0
□ the histogram has 1 cluster.
□ the histogram has 2 clusters.
□ the histogram has 1 peak.
□ the histogram has 4 peaks.
□ the histogram has 0 frequency from 4-5.

Explanation:

Step1: Organize the data

First, we list out the data values: \(0,1,1,1,2,6,6,7,8,8\).

Step2: Analyze clusters

A cluster is a group of data points that are close together. Here, we have two groups: \(\{0,1,1,1,2\}\) (lower - value cluster) and \(\{6,6,7,8,8\}\) (higher - value cluster).

Step3: Analyze peaks

A peak is a local maximum in the frequency distribution. In the lower - value cluster (\(0 - 3\) range), the mode (most frequent value) is \(1\) (frequency \(3\)). In the higher - value cluster (\(6 - 9\) range), the modes are \(6\) (frequency \(2\)) and \(8\) (frequency \(2\)). But if we consider the overall shape, we can think of two main "humps" (the lower - value group and the higher - value group), so we can say there are 2 peaks in a sense of two main clusters.

Step4: Analyze frequency in the \(4 - 5\) range

Looking at the data values \(0,1,1,1,2,6,6,7,8,8\), there are no values in the \(4 - 5\) range.

Answer:

The histogram has 2 clusters, the histogram has 2 peaks (if we consider the two - cluster structure as two peaks in a broad sense), the histogram has 0 frequency from \(4 - 5\).