If scores of a sample are distributed as 4, 6, 8, 3, 7, 8, 3, 9, 6, the mean is?

Appeared in: IGNOU PB Bsc Nsg Entrance-2017

Explanation

The mean is the statistical average of a set of numbers.
It is calculated by finding the sum of all values and dividing by the total number of values.
In this case, the sum of the scores is 4 + 6 + 8 + 3 + 7 + 8 + 3 + 9 + 6 = 54.
There are 9 scores in total.
Therefore, the mean is 54 divided by 9, which equals 6.

Option B: The number 8 is one of the modes of the dataset, meaning it is one of the most frequently occurring values (it appears twice). However, the mode is not the same as the mean.
Option C: The number 7 is a value present in the dataset, but it does not represent the mean, median, or mode. It is simply one of the data points.
Option D: The number 9 is the maximum (highest) value in the dataset. The maximum value is a measure of range, not central tendency.

Clinical Relevance

Nursing practice connection: This is primarily an exam-oriented knowledge point with limited direct bedside application, so retain Calculation of the mean (average) for a set of data as background academic context rather than a clinical decision trigger.
Understanding basic statistics like the mean is crucial for nurses to interpret medical research, patient data, and lab reports.
Nurses use averages to understand trends in a patient's vital signs (e.g., mean arterial pressure) or to evaluate the effectiveness of an intervention across a group of patients.
What if? - If the score '3' was incorrectly entered and should have been '21', the mean would drastically change to (54 - 3 + 21) / 9 = 72 / 9 = 8. This shows how the mean is sensitive to outliers or extreme values.

How to Approach the Question

First, identify the specific statistical measure the question is asking for, which is the 'mean'.
Recall the definition and formula for the mean: Mean = (Sum of all values) ÷ (Number of values).
Carefully add all the numbers provided in the dataset: 4 + 6 + 8 + 3 + 7 + 8 + 3 + 9 + 6.
Double-check the sum to avoid calculation errors. The sum is 54.
Count the total number of scores in the list. There are 9 scores.
Perform the final division: 54 ÷ 9 = 6.

Concept Tested & Keywords

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E6 NursingResearch Sukhpal Kaur pp. 442-444, 441-443

E6 Psychology Morgan King 9e Part 2 p. 332-334

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