In Exercises 5 and 6, construct the dotplot.


Pulse Rates Listed below are pulse rates (beats per minute) of females selected from Data Set 1 “Body Data” in Appendix B. All of those pulse rates are even numbers. Is there a pulse rate that appears to be an outlier? What is its value?

Verified step by step guidance

1. Step 1: Organize the pulse rates in ascending order to make it easier to identify patterns and potential outliers. The ordered data is: 36, 56, 56, 58, 60, 64, 64, 64, 66, 66, 66, 66, 76, 76, 78, 78, 78, 78, 80, 82, 84, 86, 86, 88, 94.
2. Step 2: Construct a dotplot by plotting each pulse rate value on a horizontal axis, with the number of dots above each value corresponding to its frequency in the dataset. This visual representation will help identify any values that stand out significantly from the rest.
3. Step 3: Calculate the interquartile range (IQR) to determine the range of typical values. First, find the first quartile (Q1) and third quartile (Q3) of the data. Q1 is the median of the lower half of the data, and Q3 is the median of the upper half. Then, compute the IQR using the formula: $\mathrm{IQR}=Q3-Q1$.
4. Step 4: Use the IQR to identify potential outliers. Any value that is below $Q1-1.5\times \mathrm{IQR}$ or above $Q3+1.5\times \mathrm{IQR}$ is considered an outlier.
5. Step 5: Compare the pulse rates to the calculated thresholds for outliers. Identify any values that fall outside these thresholds and confirm whether they are outliers. Highlight the outlier value, if any, based on this analysis.

Key Concepts

Dot Plot

A dot plot is a simple graphical display used to represent the frequency of data points in a dataset. Each data point is represented by a dot above a number line, allowing for easy visualization of the distribution, clusters, and gaps in the data. In this exercise, constructing a dot plot of pulse rates will help identify patterns and potential outliers.

Outlier

An outlier is a data point that significantly differs from other observations in a dataset. It can be unusually high or low compared to the rest of the data. Identifying outliers is crucial as they can skew statistical analyses and affect interpretations. In the context of pulse rates, determining if any value stands out as an outlier will provide insights into the overall health data.

Pulse Rate

Pulse rate, measured in beats per minute (BPM), indicates the number of times the heart beats in a minute. It is a vital sign used to assess cardiovascular health. In this exercise, analyzing the pulse rates of females will help understand the typical range and identify any abnormal values that may indicate health issues or anomalies.