# CUNY New York City College of Technology Statistical Data Discussion

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CUNY New York City College of Technology

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1. Statistical data plays a central role in the modern world. It is used to determine everything from the likelihood that a disease will spread in an area to the safety rating of a new type of car. It is important to understand the different measures of central tendency to make appropriate statistical decisions. The mean, the median, and the mode are the three most popular measures of central tendency. It is helpful to understand the characteristics of each to draw correct conclusions when using them.

The mean is the most commonly used measure of central tendency. It is computed by summing all the observations and dividing them by the number of observations in the sample. The median divides a list into two equal parts and lies between the values. Lastly, modes are simply data points that occur most often. The mean is the most commonly used measure of central tendency because it can show the distribution center and its variability (Rosidah & Ikram, 2021). As the name suggests, the median divides a list of points into two equal parts and lies between the two. The mode is simply the data point that appears most often.

The mode is the most standard measure of central tendency. This statistical concept can help to understand prevalent characteristics in data that might not be captured in other measures (Rosidah & Ikram, 2021). For example, if we looked at the height of adult women in America, the mean might be 60 inches, but there would be a lot of variation from person to person. The mode might be 5'6" because this is the most common height for adult women in America. The mode can also tell us about the outliers or extreme values within a distribution. For example, if we consider sales of a new product, the mean might be \$300 million, but there is a \$20 billion outlier. The median sale might be \$500 million with no outliers. However, in this case, the mode is also \$20 billion because it happens to be the value that appears most often.

The mean, median, and mode are often used interchangeably. However, it can be confusing because sometimes they are used to mean slightly different things. For example, considering height in adult women might mean 5'6", 60", or 6". Considering the number of times something is mentioned, it might mean 10, 25, or 100. To avoid confusion and make it clear to the reader that two measures of central tendency are being used, it is helpful to define each measure and how they are used in a given context. The mean, median, and mode describe the center of distribution as well as its variability. It is important to remember that the mean can also be considered the average, the median as the middle value, and the mode as the most common data point. They all help in making decisions that are based on data.

References

Rosidah, R., & Ikram, F. Z. (2021). Measure of Central Tendency: Undergraduate students’ error in decision-making perspective. International Journal of Education, 14(1), 39–47. https://doi.org/10.17509/ije.v14i1.29408

2.According to (Statistical Language - Measures of Central Tendency, n.d.) “There are three main measures of central tendency: the mode, the median, and the mean”. Each measure indicates where the center point falls within a distribution. The three measures calculate the central point using different methods. Knowing which method to use can be challenging because an individual must fully understand their data type.

Mean:

Mean is “the average or the most common value in a collection of numbers” (Mean, 2022).  To determine the mean, you must add all given values together and divide the sum by the number of values present “see equation 1.”  The calculation of the mean includes all the values in a data set. Typically, the mean does not always locate the central point accurately. It is best to use the mean to calculate the center point when you have continuous data or a more symmetric distribution. As (When to Use Mean Vs. Median (With Examples), 2021) states “It’s best to use the mean when the distribution of the data values is symmetrical and there are no clear outliers.”

Equation 1: The mathematical equation to calculate the mean.

Median:

“In Mathematics, the median is defined as the middle value of a sorted list of numbers” (Mean, n.d.).  To calculate the median, you must organize your data points from smallest to largest and determine which data point has an equal number of values below it and above it. The method of finding the median varies if your data set has an even or odd number of values. “It’s best to use the median when the distribution of data values is skewed or when there are clear outliers” (When to Use Mean Vs. Median (With Examples), 2021).

Mode:

According to (General Data Protection Regulation (GDPR) Guidelines BYJU’S, 2021) “the mode is the value that is repeatedly occurring in a given set.” Depending on your data set the mode can appear differently. For example, let’s say you have a bar chart. The mode would be the highest bar. If you have a data set with an equal number of values, then you have a multi- model and if your data has no repeating values then there is no mode. It is best to use mode when you have a probability distribution plot, ordinal data, categorical data, and count data.

In summary, understanding your data type is vital when determining which method to use to calculate a central tendency. Central tendency is important because “It lets us know what is normal or 'average' for a set of data. It also condenses the data set down to one representative value, which is useful when you are working with large amounts of data” (Williams & Clayton, 2021).

References:

General Data Protection Regulation(GDPR) Guidelines BYJU’S. (2021, March 22). BYJUS. https://byjus.com/maths/mode/

Mean. (n.d.). Retrieved October 27, 2022, from https://www.mathsisfun.com/definitions/mean.html

Mean. (2022, January 30). CFI Education Inc. https://corporatefinanceinstitute.com/resources/kn...

Statistical Language - Measures of Central Tendency. (n.d.). Retrieved October 26, 2022, from https://www.abs.gov.au/websitedbs/D3310114.nsf/Hom...

When to Use Mean vs. Median (With Examples). (2021, May 12). Statology. https://www.statology.org/when-to-use-mean-vs-medi...

• Williams, Y., & Clayton, J. (2021, August 31). Central Tendency: Measures, Definition & Examples. Study.com. https://study.com/academy/lesson/central-tendency-measures-definition-examples.

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