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# Measures of Central Tendency

Use MS Word to complete “Questions to be Graded: Exercise 8” in Statistics for Nursing Research: A Workbook for Evidence-Based Practice. Submit your work in SPSS by copying the output and pasting into the Word document.

In addition to the SPSS output, please include explanations of the results where appropriate. See attachment bellow for Data and Pictures to respond the following questions.

1. The number of nursing students enrolled in a particular nursing program between the years of 2010 and 2016, respectively, were 563, 593, 606, 520, 563, 610, and 577. Determine the mean ( X ), median ( MD ), and mode of the number of the nursing students enrolled in this program. Show your calculations.

2. What is the mode for the variable inpatient complications in Table 2 of the Winkler et al. (2014) study? What percentage of the study participants had this complication?

3. Does the distribution of inpatient complications have a single mode, or is this distribution bimodal or multimodal? Provide a rationale for your answer.

4. As reported in Table 1 , what are the three most common cardiovascular medical history events in this study, and why is it clinically important to know the frequency of these events?

5. What are the mean and median lengths of stay (LOS) for the study participants?

6. Are the mean and median for LOS similar or different? What might this indicate about the distribution of the sample? Provide a rationale for your answer.

7. Examine the study results and determine the mode for arrhythmias experienced by the partici-pants. What was the second most common arrhythmia in this sample?

8. Was the most common arrhythmia in Question 7 related to LOS? Was this result statistically signiﬁcant? Provide a rationale for your answer.

9. What study variables were independently predictive of the 50 premature ventricular contractions (PVCs) per hour in this study?

10. In Table 1 , what race is the mode for this sample? Should these study ﬁndings be generalized to American Indians with ACS? Provide a rationale for your answer.

Measures of Central Tendency: Mean, Median, and Mode – Exercise 8

## STATISTICAL TECHNIQUE IN REVIEW :

Mean, median, and mode are the three measures of central tendency used to describe study variables. These statistical techniques are calculated to determine the center of a distribution of data, and the central tendency that is calculated is determined by the level of measurement of the data (nominal, ordinal, interval, or ratio; see Exercise 1 ). The mode is a category or score that occurs with the greatest frequency in a distribution of scores in a data set.

The mode is the only acceptable measure of central tendency for analyzing nominal-level data, which are not continuous and cannot be ranked, compared, or sub-jected to mathematical operations. If a distribution has two scores that occur more fre-quently than others (two modes), the distribution is called bimodal .

A distribution with more than two modes is multimodal ( Grove, Burns, & Gray, 2013 ). The median ( MD ) is a score that lies in the middle of a rank-ordered list of values of a distribution. If a distribution consists of an odd number of scores, the MD is the middle score that divides the rest of the distribution into two equal parts, with half of the values falling above the middle score and half of the values falling below this score. In a distribu-tion with an even number of scores, the MD is half of the sum of the two middle numbers of that distribution.

If several scores in a distribution are of the same value, then the MD will be the value of the middle score. The MD is the most precise measure of central ten-dency for ordinal-level data and for nonnormally distributed or skewed interval- or ratio-level data. The following formula can be used to calculate a median in a distribution of scores.

Thus in the second example, the median is halfway between the 20 th and the 21 st scores. The mean ( X ) is the arithmetic average of all scores of a sample, that is, the sum of its individual scores divided by the total number of scores. The mean is the most accurate measure of central tendency for normally distributed data measured at the interval and ratio levels and is only appropriate for these levels of data (Grove, Gray, & Burns, 2015). In a normal distribution, the mean, median, and mode are essentially equal (see Exercise 26 for determining the normality of a distribution).

The mean is sensitive to extreme scores such as outliers. An outlier is a value in a sample data set that is unusually low or unusually high in the context of the rest of the sample data. If a study has outliers, the mean is most affected by these, so the median might be the measure of central tendency included in the research report ( Plichta& Kelvin, 2013 ). The formula for the mean is:

### RESEARCH ARTICLE

Source Winkler, C., Funk, M., Schindler, D. M., Hemsey, J. Z., Lampert, R., & Drew, B. J. (2013). Arrhythmias in patients with acute coronary syndrome in the ﬁ rst 24 hours of hospital-ization. Heart & Lung, 42 (6), 422–427.

Introduction Winkler and colleagues (2013) conducted their study to describe the arrhythmias of a population of patients with acute coronary syndrome (ACS) during their ﬁ rst 24 hours of hospitalization and to explore the link between arrhythmias and patients ’ outcomes. The patients with ACS were admitted through the emergency department (ED), where a Holter recorder was attached for continuous 12-lead electrocardiographic (ECG) moni-toring.

The ECG data from the Holter recordings of 278 patients with ACS were analyzed. The researchers found that “approximately 22% of patients had more than 50 premature ventricular contractions (PVCs) per hour. Non-sustained ventricular tachycardia (VT) occurred in 15% of the patients . . . . Only more than 50 PVCs/hour independently pre-dicted an increased length of stay ( p< 0.0001). No arrhythmias predicted mortality. Age greater than 65 years and a ﬁ nal diagnosis of acute myocardial infarction (AMI) indepen-dently predicted more than 50 PVCs per hour ( p = 0.0004)” ( Winkler et al., 2013 , p. 422).

Winkler and colleagues (2013 , p. 426) concluded: “Life-threatening arrhythmias are rare in patients with ACS, but almost one quarter of the sample experienced isolated PVCs. There was a signiﬁ cant independent association between PVCs and a longer length of stay (LOS), but PVCs were not related to other adverse outcomes. Rapid treatment of the underlying ACS should remain the focus, rather than extended monitoring for arrhythmias we no longer treat.”

Relevant Study Results The demographic and clinical characteristics of the sample and the patient outcomes for this study are presented in this exercise. “The majority of the patients ( n = 229; 83%) had a near complete Holter recording of at least 20 h and 171 (62%) had a full 24 h recorded. We included recordings of all patients in the analysis. The mean duration of continuous 12-lead Holter recording was 21 ± 6 (median 24) h. The mean patient age was 66 years and half of the patients identiﬁed White as their race ( Table 1 ).

There were more males than females and most patients (92%) expe-rienced chest pain as one of the presenting symptoms to the ED. Over half of the patients experienced shortness of breath (68%) and jaw, neck, arm, or back pain (55%). Hyperten-sion was the most frequently occurring cardiovascular risk factor (76%), followed by hypercholesterolemia (63%) and family history of coronary artery disease (53%). A major-ity had a personal history of coronary artery disease (63%) and 19% had a history of arrhythmias” ( Winkler et al., 2013 , pp. 423–424). Winkler et al. (2013 , p. 424) also reported:

“We categorized patient outcomes into four groups: 1) inpatient complications (of which some patients may have experienced more than one); 2) inpatient length of stay; 3) readmission to either the ED or the hospital within 30-days and 1-year of initial hospitalization; and 4) death during hospitalization, within 30-days, and 1-year after discharge ( Table 2 ). These are outcomes that are reported in many contemporary studies of patients with ACS. Thirty-two patients (11.5%) were lost to 1-year follow-up, resulting in a sample size for the analysis of 1-year outcomes of 246 patients” ( Winkler et al., 2013 , p. 424).

Last Updated on February 11, 2019

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