Quartile in Statistics

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The document discusses quartiles, which divide a data set into four equal parts. The first quartile contains the smallest 25% of values, the second quartile contains values between the 25th and 50th percentiles, the third quartile contains values between the 50th and 75th percentiles, and the fourth quartile contains the largest 25% of values. Formulas are provided for calculating the lower quartile (Q1), median (Q2), and upper quartile (Q3). The quartile deviation is defined as half the distance between Q3 and Q1, while the interquartile range is the full distance between Q3 and Q1. Examples are given to illustrate quartile calculations.

EDUCATIONAL STATISTICS
QUARTILE
Dr. Hina Jalal
hinansari23@gmail.com

IN STATISTICS, A QUARTILE IS A TYPE OF QUANTILE WHICH
DIVIDES THE NUMBER OF DATA POINTS INTO FOUR PARTS,
OR QUARTERS, OF MORE-OR-LESS EQUAL SIZE
Dr. Hina Jalal (hinansari23@gmail.com)

1. First quartile: 25% from smallest to
largest of numbers
2. Secondquartile: between 25.1% and
50% (till median)
3. Third quartile: 51% to 75% (above the
median)
4. Fourth quartile: 25% of largest numbers
Dr. Hina Jalal (hinansari23@gmail.com)

DIVISION OF QUARTILE
Dr. Hina Jalal (hinansari23@gmail.com)

CALCULATING LOWER, MIDDLE, & UPPER QUARTILE
 Q1 = [(n+1)/4]th item
 Q2 = [(n+1)/2]th item
 Q3 = [3(n+1)/4]th item
Hence, the formula for quartile can be given by;
Where, Qr is the rth quartile
l1 is the lower limit
l2 is the upper limit
f is the frequency
c is the cumulative frequency of the class preceding the quartile
class.
Dr. Hina Jalal (hinansari23@gmail.com)

QUARTILE FOR GROUPED DATA
Dr. Hina Jalal (hinansari23@gmail.com)

Example 1
Dr. Hina Jalal (hinansari23@gmail.com)

Example 2
Dr. Hina Jalal (hinansari23@gmail.com)

Example 3
Dr. Hina Jalal (hinansari23@gmail.com)

QUARTILE DEVIATION
 You have learned about standard deviation in statistics. Quartile deviation is defined as half
of the distance between the third and the first quartile. It is also called Semi Interquartile
range. If Q1 is the first quartile and Q3 is the third quartile, then the formula for deviation is
given by;
 Quartile deviation = (Q3-Q1)/2
Dr. Hina Jalal (hinansari23@gmail.com)

INTERQUARTILE RANGE
 The interquartile range (IQR) is the difference between the upper and lower quartile of a
given data set and is also called a midspread. It is a measure of statistical distribution, which
is equal to the difference between the upper and lower quartiles. Also, it is a calculation of
variation while dividing a data set into quartiles. If Q1 is the first quartile and Q3 is the third
quartile, then the IQR formula is given by;
 IQR = Q3 – Q1
Dr. Hina Jalal (hinansari23@gmail.com)

Dr. Hina Jalal
@AksEAina (hinansari23@gmail.com)

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This document discusses test development and evaluation. It outlines the objectives of the unit which are to highlight the role of assessment, discuss factors in selecting question types, describe reporting test scores, define objectives and outcomes, and explain techniques used in education. It then covers determining the behaviors to be assessed, developing test norms, planning the test, ensuring content validity, constructing a table of specification based on Bloom's Taxonomy, and writing supply and selection test items based on the table of specification. The document is authored by the Department of Secondary Teacher Education at Allama Iqbal Open University in Islamabad.

TEST DEVELOPMENT AND EVALUATION (6462)HennaAnsari

This document discusses test development and evaluation. It begins by outlining the objectives of the unit, which are to understand the purpose, need, scope and types of tests, as well as their role in educational measurement. It then discusses the purpose and need for tests, including for selection decisions, student classification, grading, monitoring performance, diagnosis and guidance. It describes the concept of testing and differentiates between formative and summative evaluation. It outlines the types of tests, including essay, objective, supply type and selection type questions. It discusses the significance of objective and subjective tests and provides examples of renowned tests like the SAT, GRE and Iowa Tests of Basic Skills.

Test Development and Evaluation HennaAnsari

This document discusses evaluating student progress. It begins by outlining the objectives of the unit, which are to define evaluation, describe methods of measuring student progress, analyze the need for evaluation, and discuss tools and using evaluation for instructional feedback. It then covers key concepts around evaluation including defining it as a systematic process of collecting and analyzing data to make decisions. It also discusses using both informal and formal evaluation for different purposes like informing teaching and judging student achievement. Overall, the document emphasizes that evaluation is an important part of the educational process that can provide feedback to improve instruction and measure student learning.

Factor analysis in AMOSHennaAnsari

The document provides instructions for conducting factor analysis in AMOS by first entering data in SPSS and running factor analysis to identify suggested variables, then opening AMOS to draw a framework based on the suggested variables and add the SPSS data. It describes creating a measurement model relating unique variables to latent variables and a structural model between latent variables, and checking that estimates, significance levels, and fit indices meet specified thresholds to identify an overidentified model.

Variance mean and intercept in AMOSHennaAnsari

The document provides instructions for calculating estimated means, variances, and intercepts in AMOS. It explains that after adding SPSS data, users should go to the analysis properties and select "estimate means and intercepts" in the estimation tab. Users then click "calculate estimates" which will display the estimated means and variances of exogenous variables, intercepts above endogenous variables, and covariances at double-headed arrows.

Linear regression AMOS (R-Square)HennaAnsari

This document discusses calculating R-square in AMOS. R-square represents the proportion of variance in the dependent variable explained by the independent variables. To calculate R-square in AMOS, you select the output tab in analysis properties and check the squared multiple correlation option. Then, when estimates are calculated, the R-square value will be displayed at each endogenous variable. Significant paths are also verified in the AMOS output view by checking if the critical ratio value is greater than +/- 1.96.

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TEST DEVELOPMENT AND EVALUATION (6462)HennaAnsari

Test Development and Evaluation HennaAnsari

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Variance mean and intercept in AMOSHennaAnsari

Linear regression AMOS (R-Square)HennaAnsari

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