Measures of Central Tendency

Measures of Central Tendency

SPEC 430: Assessing Educational Needs and Planning for Instruction

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Dr. Erica R. Moore​

Open Ended

Why is understanding the principles of measurement important in making educational decisions?

Daily Learning Objectives

• ​—Describe the four levels of measurement

• —Given an example, determine the scale of measurement

• —Gain an understanding of how to describe data

• —Given a set of data, identify the frequency distribution, construct a frequency polygon, and identify the mean, median, mode

What is measurement?

• ​Quantifying a variable under study to get a collection of measurable data- requires rules for assigning numbers to objects

​Scales of Measurement:

3 properties exist

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1. Magnitude:  property of “moreness” – rank order

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2. Equal Intervals: Difference between 2 points at any place on the scale has the same meaning as the difference of two different points

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3. Absolute Zero:  Exists when nothing at all exists of the property being measured

Four Levels of Measurement

1. ​Nominal Scale

2. Ordinal​ Scale

3. Interval Scale

4. ​Ratio Scale

1. Nominal Scale

• Nominal: numbers reflect nothing about the properties of the object (function like a name)

  • Has no magnitude, no equal intervals, no absolute zero

  • Examples:  social security numbers, license plate numbers, numbers on sports jerseys

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* This scale represents the least meaning for educational measurement purposes

Subject | Subject

2. Ordinal Scale

• Ordinal:  The size of the numbers assigned to the objects reflect the amount of attribute the object possesses (ranking order)

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  • Has magnitude; no equal intervals, no absolute zero

  • Examples:  academic class rank, likert scale ratings

3. Interval Scale

• .Interval:  Objects are assigned numbers to reflect the amount of attribute, and the differences between those numbers reflect equal differences in the amount of the attribute being measured

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  • Has magnitude, has equal intervals, no absolute zero

  • Examples:  IQ scores, calendar time, temperature scales

4. Ratio Scale

• Ratio:  Allows for direct comparisons and mathematical manipulations

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  • Have magnitude, equal intervals, and absolute zero

  • Examples:  Measure of speed, height, weight, time

​Kahoot Activity

​https://create.kahoot.it/share/scales-of-measurement-practice/5df642d6-3af4-44f2-83fc-08928bc65999

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​2 Types of Statistics

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​Frequency Distribution

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• Graph representation of the frequency distribution

• Normal distribution- bell curve

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• Scores on horizontal axis, frequency on vertical axis

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​Frequency Polygon

Draw

Data Set: —72, 72, 72, 78, 80, 85, 85, 85, 85, 88, 90, 90, 90, 90, 90,

• Statistical way of observing data cluster together around the average score

• 3 measures: Mean, median, mode

• Normal Distribution

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Measures of Central Tendency

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• If extreme scores, drop extreme scores before calculating the mean, otherwise skewness will occur

• Symbols: x  (for samples);

M or μ (for populations)

• Average score

• Most commonly used measure of central tendency

• Best measure of typical (average) performance

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​Mean

Open Ended

Calculate the mean: —55, 72, 78, 84, 85, 88, 90, 91, 95, 98

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• Generally found between the mean and the mode: sometimes the median is not a whole number

• Example: 1,3,5,7,9  median= 5

• Example:  0,1,2,7,8,9 median= 4.5 (add middle pair/2)

• Symbol:  Mdn or Md

• Middlemost score in a set of data

• Point on the scale below which and above which half the scores fall

• Equal to the 50th percentile, 2nd quartile

• When even number of scores: median is half way between middle two numbers​

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​Median

Open Ended

Find the median: —55, 54, 62, 72, 78, 84, 85, 88, 90, 91, 92,93, 95, 98

• Example:  3,5,5,5,7,8 (single mode)

• Example: 2,3,3,3,4,5,6,7,7,7,8  (bimodal)

• Multimodal: three or more modes

• The most frequently occurring score

• Bimodal: two modes-when a distribution has two most frequently occurring scores

• Symbol:  Mo

​Mode

Open Ended

Identify the mode: 55, 60, 60, 75, 75, 80, 90, 95

​Independent Activity

—Given a data set, students will:

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• —Rank order data set

• —Determine Frequency Distribution

• —Construct a Frequency Polygon

• —Identify mean, median, and mode

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​Ticket out the Door

—Identify the following measurement scales:

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• Percentile Ranks

• Temperature

• Weight