Measures of Central Tendency Mean, Median, and Mode Statistical Technique in Rev
ID: 3050005 • Letter: M
Question
Measures of Central Tendency
Mean, Median, and Mode
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. 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 subjected to mathematical operations. If a distribution has two scores that occur more frequently 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 distribution 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 tendency 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 20th and the 21st 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. 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:
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 first 24 hours of hospitalization. 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 first 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) monitoring. 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 predicted an increased length of stay (p < 0.0001). No arrhythmias predicted mortality. Age greater than 65 years and a final diagnosis of acute myocardial infarction (AMI) independently 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 significant 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%) experienced 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%). Hypertension was the most frequently occurring cardiovascular risk factor (76%), followed by hypercholesterolemia (63%) and family history of coronary artery disease (53%). A majority had a personal history of coronary artery disease (63%) and 19% had a history of arrhythmias” (Winkler et al., 2013, pp. 423–424).
TABLE 1
DEMOGRAPHIC AND CLINICAL CHARACTERISTICS OF THE SAMPLE (N = 278)
Characteristic
N
%
Gender
Male
158
57
Female
120
43
Race
White
143
51
Asian
60
22
Black
50
18
American Indian
23
8
Pacific Islander
2
<1
Presenting Symptoms to the ED (May Have >1)
Chest pain
255
92
Shortness of breath
189
68
Jaw, neck, arm, or back pain
152
55
Diaphoresis
116
42
Nausea and vomiting
96
35
Syncope
11
4
Cardiovascular Risk Factors (May Have >1)
Hypertension
211
76
Hypercholesterolemia
175
63
Family history of CAD
148
53
Diabetes
81
29
Smoking (current)
56
20
Cardiovascular Medical History (May Have >1)
Personal history of CAD
176
63
History of unstable angina
124
45
Previous acute myocardial infarction
114
41
Previous percutaneous coronary intervention
85
31
Previous CABG surgery
54
19
History of arrhythmias
53
19
Final Diagnosis
Unstable angina
180
65
Non-ST elevation myocardial infarction
74
27
ST elevation myocardial infarction
24
9
Interventions during 24-h Holter Recording
PCI 90 min of ED admission
14
5
PCI > 90 min of ED admission
3
1
Thrombolytic medication
3
1
Interventions Any Time during Hospitalization
PCI
76
27
Treated with anti-arrhythmic medication
16
6
CABG surgery
22
8
Mean (SD)
Median
Range
Age (years)
66 (14)
66
30–102
ECG recording time (hours)
21 (6)
24
2–25
ED, emergency department; CAD, coronary artery disease; CABG, coronary artery bypass graft; PCI, percutaneous coronary intervention; SD, standard deviation; ECG, electrocardiogram.
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 first 24 hours of hospitalization. Heart & Lung, 42(6), p. 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).
TABLE 2
OUTCOMES DURING INPATIENT STAY, AND WITHIN 30 DAYS AND 1 YEAR OF HOSPITALIZATION (N = 278)
Outcomes
N
%
Inpatient complications (may have >1)
AMI post admission for patients admitted with UA
21
8
Transfer to intensive care unit
17
6
Cardiac arrest
7
3
AMI extension (detected by 2nd rise in CK-MB)
6
2
Cardiogenic shock
5
2
New severe heart failure/pulmonary edema
2
1
Readmission
30-day
To ED for a cardiovascular reason
42
15
To hospital for ACS
13
5
1-year (N = 246)
To ED for a cardiovascular reason
108
44
To hospital for ACS
24
10
All-cause mortality
Inpatient
10
4
30-day
13
5
1-year (N = 246)
27
11
Mean (SD)
Median
Range
Length of stay (days)
5.37 (7.02)
4
1–93
*Readmission: 1-year data include 30-day data.
† All-cause mortality: 30-day data include inpatient data; 1-year data include both 30-day and inpatient data.
AMI, acute myocardial infarction; UA, unstable angina; CK-MB, creatinine kinase-myocardial band; ED, emergency department; ACS, acute coronary syndrome; SD, standard deviation.
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 first 24 hours of hospitalization. Heart & Lung, 42(6), p. 424.
Study Questions
In Table 1, what is the mode for cardiovascular risk factors? What percentage of the patients experienced this risk factor?
Characteristic
N
%
Gender
Male
158
57
Female
120
43
Race
White
143
51
Asian
60
22
Black
50
18
American Indian
23
8
Pacific Islander
2
<1
Presenting Symptoms to the ED (May Have >1)
Chest pain
255
92
Shortness of breath
189
68
Jaw, neck, arm, or back pain
152
55
Diaphoresis
116
42
Nausea and vomiting
96
35
Syncope
11
4
Cardiovascular Risk Factors (May Have >1)
Hypertension
211
76
Hypercholesterolemia
175
63
Family history of CAD
148
53
Diabetes
81
29
Smoking (current)
56
20
Cardiovascular Medical History (May Have >1)
Personal history of CAD
176
63
History of unstable angina
124
45
Previous acute myocardial infarction
114
41
Previous percutaneous coronary intervention
85
31
Previous CABG surgery
54
19
History of arrhythmias
53
19
Final Diagnosis
Unstable angina
180
65
Non-ST elevation myocardial infarction
74
27
ST elevation myocardial infarction
24
9
Interventions during 24-h Holter Recording
PCI 90 min of ED admission
14
5
PCI > 90 min of ED admission
3
1
Thrombolytic medication
3
1
Interventions Any Time during Hospitalization
PCI
76
27
Treated with anti-arrhythmic medication
16
6
CABG surgery
22
8
Mean (SD)
Median
Range
Age (years)
66 (14)
66
30–102
ECG recording time (hours)
21 (6)
24
2–25
Explanation / Answer
Answer:
In Table 1, what is the mode for cardiovascular risk factors? What percentage of the patients experienced this risk factor?
Cardiovascular Risk Factors (May Have >1)
N
%
Hypertension
211
76
Hypercholesterolemia
175
63
Family history of CAD
148
53
Diabetes
81
29
Smoking (current)
56
20
Highest Number of patients with cardiovascular risk factors is Hypertension = 211
Percentage of the patients experienced Hypertension = 76%
Cardiovascular Risk Factors (May Have >1)
N
%
Hypertension
211
76
Hypercholesterolemia
175
63
Family history of CAD
148
53
Diabetes
81
29
Smoking (current)
56
20