Using StatCrunch, report back to the class the mean, median, and standard deviation for the following heart rate values: 136, 144, 99, 145, 135, 125, 115, 127, 124, 101, 100, 103,... Using StatCrunch, report back to the class the mean, median, and standard deviation for the following heart rate values: 136, 144, 99, 145, 135, 125, 115, 127, 124, 101, 100, 103, 130, 119, 121, 123, 116, 115, 126, 114, 125, 125, 116, 137, 152. Graph the data as a histogram with a fit to a normal curve and include this in your Word document. Compute the z-score for the heart rate of 127.
Understand the Problem
The question involves analyzing a set of heart rate data collected from a medical school class. It requires calculating statistical measures such as mean, median, and standard deviation using StatCrunch, generating a histogram with a normal curve fit, and computing a z-score based on one student's heart rate compared to the rest of the data. This is a comprehensive statistical analysis task.
Answer
The steps involve calculating mean, median, standard deviation, creating a histogram, and finding z-scores.
Answer for screen readers
The results of the calculations (mean, median, standard deviation, z-score) will depend on the specific heart rate data provided. Please calculate those values based on your dataset.
Steps to Solve
- Calculate the Mean Heart Rate
To calculate the mean (average) heart rate, sum all the heart rate values and divide by the number of values. If the heart rates are: $HR_1, HR_2, \ldots, HR_n$, then the formula for mean is:
$$ \text{Mean} = \frac{HR_1 + HR_2 + \ldots + HR_n}{n} $$
- Calculate the Median Heart Rate
To find the median, first, arrange the heart rate values in ascending order. If there are an odd number of values, the median is the middle number. If there are an even number of values, the median is the average of the two middle numbers.
- Calculate the Standard Deviation
The standard deviation measures the amount of variation in the heart rates. To calculate it, use the formula:
$$ \text{Standard Deviation} = \sqrt{\frac{\sum (HR_i - \text{Mean})^2}{n}} $$
where $HR_i$ represents each heart rate value.
- Generate a Histogram with Normal Curve Fit
Use StatCrunch or similar statistical software to create a histogram of the heart rate data. Ensure to select the option to overlay a normal curve that fits the data.
- Calculate the Z-Score for One Student's Heart Rate
To find the z-score of a specific student's heart rate ($HR_{student}$), use the formula:
$$ z = \frac{HR_{student} - \text{Mean}}{\text{Standard Deviation}} $$
This will indicate how far the student's heart rate is from the mean in terms of standard deviations.
The results of the calculations (mean, median, standard deviation, z-score) will depend on the specific heart rate data provided. Please calculate those values based on your dataset.
More Information
Calculating the mean, median, and standard deviation helps understand the central tendency and spread of the heart rate data. The z-score allows you to assess how unusual a specific heart rate is compared to the average.
Tips
- Not arranging the data properly for the median calculation.
- Confusing population standard deviation with sample standard deviation.
- Misinterpreting the z-score, which indicates how many standard deviations an element is from the mean.
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