Central Tendency is commonly referred to as the "measure of central tendency". A measure of central tendency is used to describe a data set by identifying the central position within that set of data. In statistics, the three most commonly used measures of central tendency are mean, median, and mode.

Mean: The mean is the average of all the numbers within a data set. To find the mean value, one would add up all the values in a data set and divide that sum by the total number of data points within the data set.
Example - 3+4+5+6+7 = 25. There are 5 values in this data set. 25/5 = 5. In this scenario the mean, or average, is 5.

Median: The median is the middle point in a sorted set of data. The median is identified by organizing the data set into order of magnitude (starting with the smallest number).
Once sorted the median is identified as the number directly in the middle of that sorted data.
Example - 6, 9, 23, 15, 2. If we put this data set in order by magnitude it is displayed as: 2, 6, 9, 15, 23. In this data set 9 is the median.

Mode: The mode is the number that occurs most frequently in a data set.
Example - 2, 3, 15, 3, 5, 7, 8, 3, 2, 1, 10, 9.
In this data set, 3, is the number that occurs most frequently and would be identified as the mode.

''contributed by, Scott Trungadi''

''Having finally mastered the skills necessary to report my data, and thanks to the help from fellow students in my doctoral program, I was ready to write up a description of what all the numbers meant. I was excited to have reached this point in my central tendency assignment, as there is one thing I love doing, and that is write. Finally, something I might be good at! However, this also meant that I needed to understand and be able to explain what all the numbers meant.''

In October of 2007 during the kindergarten year, the Letter Naming Fluency
( LNF) portion of the Dynamic Indicators of Basic Early Literacy Skills (Dibels) was administered to a class of 18 kindergarten students, 10 males and 8 females.
The SPSS helped to process the following data regarding the testing administration. The mean score for the eighteen students for the Beginning LNF portion of Dibels was 32.33 with the median or midpoint being 35.0(Table 1). By gender, the boys in the class scored slightly lower with the mean score of 32.30 and the midpoint or median score of 34.50 as compared to the girls’ mean score of 32.38 and a median of 37.00(Table 5).

The standard deviation is based on all the scores in the group and is determined by how much each score deviates from the mean, or in other words, it is an estimate of what the range of scores probably was. The standard deviation tells me that in the Beginning and Ending LNF administration, all students tested, in a similar range-16.01 and 16.87(Tables 1 and 2).
However, in looking at the Beginning LNF scores analyzed by gender, there is a large discrepancy between how well the boys did when compared to the girls. There was a higher standard of deviation for the boys than the girls, respectively 16.34 for the boys and 6.71 for the girls. In trying to understand the possible reasons for this, one must consider birthdates. Although birthdates were not considered in this collection of data, it is important to note that there was a higher incidence of younger birth dates for the boys than the girls which might account for this wide range in the boys’ scores.

The Z scores in this statistical analysis refer to how many standard deviations a particular raw score lies above or below the group means. Table 6 indicates the range of Z scores for the students who had taken the Ending LNF portion of the Dibels test. The score range from 1.44, or 1.44 standard deviations above the group mean of 64.67 to -1.82, or 1.82 below the group mean of 64.67.

''I actually felt that I began to really understand what everything meant as I was scripting my report. It was very helpful. Hope this helps someone!''

''contributed by Debbie Mumford''

Shapes of distribution

2019-09-23T22:44:31Z

Strungadi: /* Normal (bell-shaped) distribution */

Distribution of data can take a wide variety of shapes, and ultimately depends on how data points are distributed along the measurement scale. A general "feel" for the data can be achieved by examining the uniformity (or lack thereof) of a distribution. In general, the larger the sample size, the more symmetrical the distribution.

== Uniform distribution ==

== Normal (bell-shaped) distribution ==

When the collected data tends to hover around a central value, with no bias to the left or the right, the data creates a Normal distribution.
This Normal distribution is also referred to as the "Bell Curve" because it resembles a bell like shape.

When stating that data is normally distributed we are identifying that 50% of the values are less than the mean and that 50% of the values are greater than the mean. In a normal distribution the mean, median, and mode are equal to one another.

Examples of data that follow a normal distribution could include blood pressure and scores on a test.

''contributed by, Scott Trungadi''

== Skewness ==

Skewed right
Skewed left

Acceptable skewness values: <big>-1.000 < skewness < 1.000 </big>

Examining the data skewness allows you to see the variability of a data set. Skewness is when a data set does not follow the normal distribution. A normal distribution has a skewness of zero, and will have perfect symmetry. Data that is positively skewed will be skewed to the right and will be a positive number; data that is negatively skewed is skewed to the left of the data mean, and is a negative number. See an example of skewness, below.

"contributed by Cassandra Cosentino"

[[File:skewness.png]]

== Kurtosis ==

Leptokurtic
Platykurtic

Acceptable kurtosis values : <big>-1.000 < kurtosis < 1.000 </big>