This document discusses central tendency and various statistical measures used to analyze data distributions. It provides examples of calculating the mode, mean, median and range of a sample data set. It also explains key concepts like standard deviation, which measures how dispersed data values are from the mean, skewness, which quantifies the asymmetry of a distribution, and kurtosis, which describes the heaviness of a distribution's tails relative to a normal distribution.
Central moments, grouped data formula, ungrouped data formula, skewed distribution, skewness, kurutosis,measure of kurutosis, tyes of kurutosis, statistics, moments, statistics formula
Topic: Skewness
Student Name: Farhana Siddiqui
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Graphics displays are useful for seeing patterns in data. Patterns in data are commonly described in terms of center, spread, shape and unusual features, some common distribution have special descriptive labels, such as symmetry, bell-shaped, skewed.
Central moments, grouped data formula, ungrouped data formula, skewed distribution, skewness, kurutosis,measure of kurutosis, tyes of kurutosis, statistics, moments, statistics formula
Topic: Skewness
Student Name: Farhana Siddiqui
Class: B.Ed. 2.5
Project Name: “Young Teachers' Professional Development (TPD)"
"Project Founder: Prof. Dr. Amjad Ali Arain
Faculty of Education, University of Sindh, Pakistan
Graphics displays are useful for seeing patterns in data. Patterns in data are commonly described in terms of center, spread, shape and unusual features, some common distribution have special descriptive labels, such as symmetry, bell-shaped, skewed.
A basic task in numerous statistical analyses is to characterize the position and variability of a data set. Another characterization of the data includes skewness and kurtosis.
Skewness is a measure of balance, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the centre point.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
Normal provability curve is one of the important topic in the Educational research.The theory of parametric tests in the inferential statistics is completely based on the NPC. Every researcher must know the characteristics of the NPC.
A basic task in numerous statistical analyses is to characterize the position and variability of a data set. Another characterization of the data includes skewness and kurtosis.
Skewness is a measure of balance, or more precisely, the lack of symmetry. A distribution, or data set, is symmetric if it looks the same to the left and right of the centre point.
Kurtosis is a measure of whether the data are heavy-tailed or light-tailed relative to a normal distribution.
Normal provability curve is one of the important topic in the Educational research.The theory of parametric tests in the inferential statistics is completely based on the NPC. Every researcher must know the characteristics of the NPC.
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2. QUESTION 1.A
A. Explain the central tendency of Data: Calculate
mode, mean, median, and Range of the following:
( 10 marks)
15, 20, 21, 20, 36, 15, 25, 15.
3. CENTRAL TENDENCY
The central tendency of a distribution is an estimate
of the "center" of a distribution of values.
Central tendency is needed because often we want
one value that best represents an entire group of
scores or a number that is “typical” of the group as
a whole.
4. TYPES OF CENTRAL TENDENCY
There are three major types of estimates of central
tendency:
Mean
Median
Mode
5.
6. MEAN
The sum of these 8 values is 167, so the mean is
167/8
= 20.875.
7. MEDIAN
The Median is the score found at the exact
middle of the set of values.
There are 8 scores and score #4 and #5
represent the halfway point.
Since both of these scores are 20 and 36
So, Median is 56/2
= 28
8. MODE
The mode is the most frequently occurring
value in the set of scores
The most frequently occurring value is the
mode
In our example, the value 15 occurs three
times
So, the Mode is15
9. RANGE
The range is simply the highest value minus the
lowest value.
In our example distribution, the highest value is 36
and the lowest value is 15
So, the range is 36 - 15 = 21
11. STANDARD DEVIATION
A quantity expressing by how much the members of
a group differ from the mean value for the group.
It is a more accurate and detailed estimate of
dispersion
It is a measure that is used to quantify the amount
of variation or dispersion of a set of data values.
It is represented by the Greek letter sigma σ
13. SKEWNESS
It is a measure of the lack of symmetry (i.e
asymmetry)
Skewness is asymmetry in a statistical distribution,
in which the curve appears distorted or skewed
either to the left or to the right
The value can be positive, negative or undefined
15. KURTOSIS
It is a measure of data in a distribution
It explains whether the data are heavy-tailed or
light-tailed relative to a normal distribution
