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metrics of central tendency

RESPOND IN 300 WORDS:

Central Tendency Measures: This is a numerical method that provides a summary of the dataset. It focuses on the centralization of data delivery via a single value. Average grades, rainfall, income, and other real-life examples of metrics of central tendency The arithmetic mean, median, and mode are three often used metrics of central tendency.

There are various central tendency measurements, the most frequent of which being Mean, Median, and Mode. Let’s look at the most prevalent metrics of central tendency, which are listed below:

The sum of the values in the dataset divided by the number of observations or values equals the mean. This is also known as the arithmetic mean and is the most often used measure of central tendency. It is determined using the formula: X1 + X2+ X3 +……………….+ XN/ N

The mean for ungrouped data and the arithmetic mean for grouped data are two different forms of arithmetic means.
As an example, A monthly income for a family of four is 1600, 1400, 1300, and 1200 dollars. Determine the family’s average income.
1600 + 1400 + 1300 +1200 = 1600 + 1400 + 1300 +1200 /4 is the solution.
=1375
As a result, the family’s average monthly income is Rs. 1375.

It’s defined as the value that splits the distribution in half. The median value is larger than or equal to one portion of the values, while the other is less than or equal to the other. By organizing the data from smallest to greatest, you may calculate the median.

As an example, Find the median by arranging the data 5, 7, 6, 1, 8, 10, 12, 4, and 3 in ascending order. 1, 3, 4, 5, 6, 7, 8, 10, 12 are all numbers. The data’s median value is 6. In this case, half of the numbers are more than 6, while the other half is smaller.

If the data contains two numbers in the middle value, you can calculate it using the formula below:
1, 3, 4, 5, 6, 7, 8, 10, 12, and 13 are all numbers.
By multiplying two median values by the number of observations, this can be obtained.

The most frequently seen data value is known as mode. There’s a risk we’ll find duplicate numbers in the data set.

For instance, 1, 2, 3, 4, 4, 5, where 4 is the most commonly encountered value.

RESPOND IN 300 WORDS:

 

There are three measures of central tendency. Mean, Median, and Mode. The Mean takes a sum of numeric values and divide the numbers by the total quantity. Ex: 3, 4, 5, 6, 7 The sum of all would be 25. 25/5=5. This would be the mean.

The Median is the number in the middle of the from a set of values. Using same numbers as above the median would be 5. If there were an even number of values, the median would be the two middle numbers divided by two.

The Mode is the consistent number in a set of values. When a group of numeric numbers have no consistent numbers, then there is not be a mode. A mode however can be linked by interest as well.
Ex. A survey of top selling potato chip brands can have a mode based on highest selection chosen (Gravetter et al., 2020, P.90).

Outliners can or cannot have an effect on a median, mode, or mean. This can cause an increase, decrease, and same answer. Outliners are what stand out and may or may not affect the mode, mean and median.

You are part of a school and have to report the results of standardized test scores. Which measure of central tendency would you use?  I would likely use the mean. Although the mean, does not accurately account for each score, it can estimate the concept of understanding of the test, by the average score. The outstanding outliner could justify level of comprehensive or discipline.

Ex: Sample test scores

Anna-70                              The Mean of these scores would be 81. An outliner is 70

Brad-78                                 The Median is 80, an outliner is 70. 

Sammie-80                            The Mode is also 80, and also the outliner is 70. 

Joyce-80

Carol-82

John-84

Crystal-90

Recently, two new transfer students joined your school, and both have received extremely high scores on the test. Which measure of central tendency would you use, and why? I would still use the mean, due to this being a standardized test, and the mean can concept the level of comprehensive.

Anna-70              The Mean of these scores increased to 84

Brad-78                The Median increased is 82

Sammie-80           The Mode did not change from 80. 70 is still an outliner. 

Joyce-80

Carol-82

John-84

Crystal-90

Monique-95 Since the additional scores were a higher number, this increased the mean and median, but did not affect the mode.

Chris-97