How to Find the Mean, Median, and Mode

Understanding how to find the mean, median, and mode is essential for evaluating data in psychological research. These values provide insights into what may be considered "typical" or "deviant" with regards to particular behaviors or cognitive functions within a specific group of individuals.

Definitions of Mean, Median, and Mode:

1. Mean:

   • Definition: The mean represents the arithmetic average of a set of numerical values. It is commonly referred to as the "average."
   • Calculation:
     • Sum all the values in the given set.
     • Divide the sum by the total number of values.

2. Median:

   • Definition: The median is the middle value in a set of numerical values when arranged in order from smallest to largest.
   • Calculation:
     • Arrange the values in ascending order.
     • If the number of values is odd, the middle value is the median.
     • If the number of values is even, the median is the average of the two middle values.

3. Mode:

   • Definition: The mode is the value that occurs most frequently within a set of numerical values.
   • Calculation:
     • Identify the value that appears most often in the data set.

Calculating Mean:

Step 1: Add all the values together.

Step 2: Divide the sum by the number of values used.

For example:

Given the values: 3, 11, 4, 6, 8, 9, 6

Step 1: Add all the numbers together (3 + 11 + 4 + 6 + 8 + 9 + 6 = 47).

Step 2: Divide the total sum by the number of scores used (47 / 7 = 6.7).

Therefore, the mean or average of the given set is 6.7.

Calculating Median:

Step 1: Arrange all the data points from smallest to largest.

Step 2: If the number of scores is odd, the median is the number in the very middle of the list.

Step 3: If the number of scores is even, calculate the average of the two middle numbers.

For odd number of scores:

Given the set: 5, 9, 11, 9, 7.

Step 1: Arrange them in numerical order (5, 7, 9, 9, 11).

Step 2: Since you have an odd number of scores, the number in the third position of the data set is the median, which, in this case, is 9 (5, 7, 9, 9, 11).

For even number of scores:

Given the set: 2, 5, 1, 4, 2, 7.

Step 1: Put them in numerical order (1, 2, 2, 4, 5, 7).

Step 2: The two middle scores are 2 and 4, so add them together (2+4=6) and then divide 6 by 2, which equals 3.

Therefore, the median score for this data set is 3.

Calculating Mode:

The mode is simply the most frequently occurring score in a distribution.

Step 1: Look at all the data scores.

Step 2: Identify the data score that appears most often.

For example:

Given the distribution: 2, 3, 6, 3, 7, 5, 1, 2, 3, 9.

The mode of these numbers would be 3 since this is the most frequently occurring number (2, 3, 6, 3, 7, 5, 1, 2, 3, 9).

Pros and Cons of Mean, Median, and Mode:

1. Mean:

   • Pros: Utilizes all numbers in a set to determine the measure of central tendency.
   • Cons: Outliers can distort the overall measure.

2. Median:

   • Pros: Unaffected by outliers.
   • Cons: May not adequately represent the full set of numbers.

3. Mode:

   • Pros: Less influenced by outliers. Represents what is "typical" for a given group of numbers.
   • Cons: May be less useful when no number occurs more than once. Less informative when multiple modes exist.

When to Use Mean, Median, and Mode:

• Mean: Use the mean when there are no outliers and you want to find the average value.
• Median: Use the median when there are outliers or when you want to find the middle value.
• Mode: Use the mode when you want to find the most frequently occurring value.

Example of Mean, Median, and Mode in Psychology:

In a study on the average age of schizophrenia diagnosis, data collection from mental health providers revealed the following ages:

20, 25, 35, 27, 29, 27, 23, 31

Calculating mean, median, and mode, the values are: - Mean: 27.1 years - Median: 27 years - Mode: 27 years

In this case, any of these measures could be used to represent the typical age of onset.

However, if an additional score of 13 were introduced, the mean would be 25.6, while the median and mode would both be 27. This highlights how outliers can skew the mean, making the median and mode more accurate in this instance.

Conclusion:

Mean, median, and mode are valuable tools for analyzing psychological data. Understanding their definitions, methods of calculation, and strengths and weaknesses is essential for interpreting research findings accurately.