CHAPTER 5: KEY TERMS

1. Statistics-is a branch of science, which deals with the collection, presentation, analysis and interpretation of quantitative data.

2. Descriptive statistics -is a method concerned with collecting, describing analyzing a set of data without drawing conclusions (or inreferences) about a large group.

3. Inferential statistics -is a branch of statistic, concerned with the analysis of a subset of data leading to predictions or inreferences about the entire set of data.

4. Mean -is the most commonly used measures of the center of data and it is also referred as the “arithmetic average”

5. Median -is the second type of measures of central tendency. Median is what divides the scores in the distribution into two equal parts.

6. Variability - (also called spread or dispersion) refers to how spread out a set of data is.

7. Range -is the difference between the highest score and the lowest score in a distribution. Range is the simplest and the crudest measure of variation, simplest because we shall only considered the highest score and the lowest score.

8. Mean deviation - measures the average deviation of the values from the arithmetic mean. It gives equal weight to the deviation of every score in the distribution.

9. Quartile deviation -indicates the distance we need to go above and below the median to include the middle 50% of the score. It is based on the range of the middle 50% of the scores, instead of the range of the entire set.

10. Standard deviation- is the most important measures of variation. It is also known as the square root of the variance. It is the average distance of all the scores that deviates from the value mean.

11. Variance -is one of the most important measures of variation. It shows a variation about the mean.

12. Coefficient of variation shows variation relative to the mean.it is used to compare to two or more groups of distribution of scores.

13. Skewness -can be classified according to the skewness coefficient

14. Negative skewed or skewed to the left if Sk>o, is a distribution where the thin end tail of the graph goes to the left part of the curve.

15. Positively skewed or skewed to the right if Sk<o, is a distribution where the thin end tail of the graph goes to the right part of the curve.

16. Normal distribution is a special kind of symmetric distribution and it represents some properties in mathematics. It is very important when comparing between scores and making statistical decisions.

17. z-Score used to convert a raw score to standard score to determine how far a raw score lies from the mean in standard deviation units.

18. t- score are two possible values of z-score, positive z if the raw score is above the mean and negative z if the raw score s below the mean.

19. Percentile rank indicates the percentage of scores that lies below a given score.

20. Standard nine is a nine point grading scale ranging from 1to9, 1 being the lowest and 9 the highest.

CHAPTER EXERCISES

1. WHAT IS THE IMPORTANCE OF DIFFERENT MEASURES OF CENTRAL TENDENCY IN ASSESSING THE PERFORMANCE OF THE STUDENTS IN THE CLASSROOM?

-The importance of different measures of central tendency in assessing the performance of the students in the classroom, it provides a very convenient way of describing a set of scores with a single number that describes the performance of the group.

2. WHEN DO WE USE MEAN, MEDIAN AND MODE?

When to use the mean

*sampling stability is desired

*other measures are to be computed such as standard deviation, coefficient of variation and skewness.

When to use the median

*The exact midpoint of the score distribution is desired.* There are extreme scores in the distribution.

When to use the mode

*When the “typical” value is desired.

* When the data set is measured on a nominal scale.

3. WHAT ARE THE PROPERTIES OF MEAN, MEDIAN AND MODE?

The properties of the mean

*It measures stability. Mean is the most stable among other measures of central tendency because every score contributes to the values of the mean.

*The sum of each score’s distance from the mean is zero.

*It is easily affected by the extreme scores

* It may not be an actual score in the distribution.

*It can be applied to interval level of measurement

* It is very easy to compute.

The properties of median

*It may not be an actual observation in the data set.

*It can be applied in ordinal level.

*It is not affected by the extreme values because median is a positional measure.

The properties of mode

*It can be used when the data are qualitative a well as quantitative.*It may not be unique.*It is not affected by the extreme values.*It may not exist.

4. WHY DO MEAN, MEDIAN AND MODE USEFUL IN INTERPRETING THE PERFORMANCE OF THE STUDENTS?

* The mean of a set of test scores tells you what the

average score on the test was for the class.

*The median of a set of test scores tells you what the

middle grade is when you order the grades from highest

to lowest. The closer the median is to the mean, the

more normally distributed the data is.

5. WITH THE PRESENCE OF EXTREME SCORES IN THE DISTRIBUTION, WHAT MEASURE OF CENTRAL TENDENCY IS MORE APPROPRIATE TO INTERPRET THE RESULT?

The mean is widely preferred as the best measure of central tendency because it is the measure that includes all the values in the data set for its calculation.

6.IF THE SCORES OF THE STUDENTS IN THE TEST ARE DISTRIBUTED NORMALLY, WHAT MEASURE OF CENTRAL TENDENCY WOULD BEST DESCRIBE THEIR PERFORMANCE?

Mean and median both try to measure the central tendency in a data set.

7.WHAT MEASURES OF CENTRAL TENDENCY IS EASILY AFFECTED BY EXTREM SCORES?

-The mean is the preferred measures of central tendency

because it is more frequently in advanced statistical

procedures, however, it is also the most susceptible

to extreme scores.

8.IF THE SCORES OF THE STUDENTS ARE NOT NORMALLY DISTRIBUTED, WHAT MEASURE OF CENTRAL TENDENCY IS MORE APPROPRIATE TO DISCRIBE THEIR PERFORMANCE?

-The median is usually preferred to other measures of central tendency however, the mode can be appropriate in these situations.

12. WHAT IS MEASURE OF VARIATION OR DISPERSION?

Measures of variation is a single value that is used to describe the spread of the scores in a distribution. The term variation is also known as variability or dispersion. There several ways of describing the variation of scores.

13. WHAT ARE THE TWO TYPES OF VARIATION?

The two types of variation are

*Absolute measures of variation

*Relative measures of variation

14. WHAT ARE THE DIFFERENT TYPES OF ABSOLUTE MEASURES OF VARIATION?

*There are four kinds of absolute variation. The range, inter-quartile range and quartile deviation, mean deviation, variance and standard deviation.

15. WHAT IS COEFFICIENT OF VARIATION?

Coefficient of variation shows variation relative to the mean. It is used to compare two or more groups of distribution of scores.

Usually expressed in percent, the smaller the value of the coefficient of variation the more homogeneous the scores in that particular group.

16 .DESCRIBE THE IMPORTANCE OF THE DIFFERENT MEASURES OF VARIABILITY IN ASSESSING THE PERFORMANCE OF THE STUDENTS.

-An important use of statistics is to measure variability or the spread of data. For example, two measures of variability re the standard deviation and the range. The standard deviation measures the spread of data from the mean or the average score. Standard deviation can be useful in analyzing classroom results.

17. WHAT ARE THE DIFFERENT PROPERTIES OF THE RANGE, MEAN DEVIATION , QUARTILE DEVIATION ,INTER-QUARTILE RANGE , VARIANCE AND STANDARD DEVIATION.?

Properties of Range

*It is quick and easy to understand.

*It is a rough estimation of variation

*It is easily affected by the extreme score.

Properties of mean deviation

*Mean deviation takes its minimum value when the

deviations are taken from the median

*Mean deviation remains unchanged due to change of origin

but changes in the same ratio due to a change in

scale.

Properties of inter quartile deviation and quartile

deviation

*Reduces the influence of extreme values.

*Not as easy to calculate as the range.

*Only considers the middle 50% of the scores in the

distribution.

*The point of dispersion is the median value.

Properties of variance and standard deviation.

*The most commonly used measures of variation most

especially in research.

*It shows variation of the individual scores about mean.

18. WHAT IS THE ADVANTAGE OF STANDARD DEVIATION OVER RANGE IN IDENTIFYING THE VARIATION OF SCORES OF THE STUDENTS IN A CERTAIN TEST?

- Range gives an overall spread of data from lowest to highest of data and can be influenced by anomalies. Whereas standard deviation takes into account the variable data/ spread out about the mean and allows for statistical use so inferences can be made.

19. WHEN DO WE USE STANDARD DEVIATION AND COEFFICIENT OF VARIATION IN INTERPRETING THE DISPERSION OF SCORES?

It is used to compare two or more groups of distribution of scores. Usually expressed in percent, the smaller the value of the coefficient of variation the more homogeneous the scores in particular scores. On the other hand, the higher the value of the

coefficient of variation the more dispersed the scores in that particular distribution.

20. WHEN THE COMPUTED STANDARD DEVIATION OF THE SCORES OF THE STUDENTS IN A CERTAIN TEST IS LOW, WHAT CAN YOU SAY ABOUT DISPERSION OF THEIR PERFORMANCE? HOW ABOUT IF THE STANDARD DEVIATON IS HIGH?

-The smaller value of standard deviation on the average the closer the scores are to the mean value and the larger the value of the standard deviation on the average makes the score scattered from the mean value.

21. WHAT DOES THE DEVIATION INDICATE IN THE SCORES OF THE STUDENTS?

-The size of the standard deviation can give you information about how widely students’ scores varied from the average. A larger standard deviation means there was more variation of scores among people who took the test, while a smaller standard deviation means there was less variance

22. WHAT MEASURE OF VARIATION IS EASILY AFFECTED BY THE EXTREME SCORE?

-The properties of range.

28. WHAT IS SKEWNESS?

It can be classified according to the skewness coefficient. If Sk>0 it is called positively skewed distribution. When Sk<0, it is negatively skewed distribution. However, if Sk=0 are normally distributed.

29. WHAT ARE THE DIFFERENT KINDS OF SKEWNESS?

*Positively skewed

*Negatively skewed

30. WHAT IS DIFFRENCE BETWEEN SKEWNESS AND NORMAL DISTRIBUTION?

-The skewness of the score distribution indicates only the performance of the students but not the reasons about their performance while the normal distribution is a special kind of symmetric distribution and it represents some properties in mathematics. It is very important when comparing between scores and making statistical decisions. While in probability theory, a normal distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is The parameter is the mean or expectation of the distribution; and is its standard deviation.

32. DIFFERENTIATE POSITIVELY SKEWED DISTRIBUTION FROM NEGATIVELY SKEWED DISTRIBUTION IN TERMS OF STUDENT’S PERFORMANCE?

-In a positively skewed distribution, the mean is usually greater than the median because the few high scores tend to shift the mean to the right. In a negatively skewed, the mean is usually

less than the median because the few low scores tend to shift the mean to the left.

33. WHAT ARE THE PROPERTIES OF NEGATIVELY SKEWED DISTRIBUTION AS APPLIED TO STUDENTS’ PERFORMANCE?

- In a negatively skewed distribution, the mode is always greater than the mean and median.

34. WHAT ARE THE PROPERTIES OF POSITIVELY SKEWED DISTRIBUTION AS APPLIED TO STUDENTS’ PERFORMANCE?

-Negatively skewed distribution will always be on right side.

38. WHAT IS NORMAL DISTRIBUTION?

-normal distribution is a special kind of symmetric distribution and it represents some properties in mathematics. It is very important when comparing between scores and making statistical decisions. It can be determined using the values of the mean and standard deviation.

39. WHAT ARE THE CHARACTERISTICS OF SCORE DISTRIBUTION THAT ARE NORMALLY DISTRIBUTED?

40. WHAT ARE DIFFERENT TYPES OF CONVERTED SCORES? DISCUSS EACH AND GIVE THE FUNCTION OF EACH CONVERTED SCORE IN ANALYING THE PERFORMANCE OF THE STUDENT IN A CERTAIN EXAMINATION.

The different types of converted scores are:

z-score- Also called standard score a z-score can be placed on a normal distribution curve. Z- score range from- 3 standard deviations (which would fall to the far left of the normal distribution curve). In order to use z-score you need to know the mean and also the population standard deviation.

T-scores- type of standard score computed by multiplying by

10 and adding 50.

Stanine score- is a way to scale scores on a nine point scale. It can be used to convert any test score and t-score, stanine are a way to assign a number to a member of a group

Scaled score- the purpose of scaled scores is to report scores for all examines on a consistent scale. Suppose that a test has two forms, and one is more difficult than other one. It has been determined by the equating that a score of 65% on from 1 is equivalent to a score of 68% on form 2.

41. DIFFERENTIATE SKEWNESS FROM NORMAL CURVE.

Skewness, in basic terms, implies off-centre, so does in statistics, it means lack of symmetry. With the help of skewness, one can identify the shape of the distribution of data. Kurtosis, on the other hand, refers to the pointedness of a peak in the distribution curve. The main difference between skewness and kurtosis is that the former talks of the degree of symmetry, whereas the latter talks of the degree of peakedness, in the frequency distribution

48. WHAT IS CORRELATION?

Correlation. Correlation is a statistical technique that can show whether and how strongly pairs of variables are related. For example, height and weight are related; taller people tend to be heavier than shorter people.

49. WHAT ARE DIFFERENT TYPE OF CORRELATION? DISCUSS EACH TYPE.

Types of Correlations

Broadly speaking there are three different types of correlations: positive, negative, and neutral or no correlation. A perfect positive correlation would mean that if you increased the one variable by one unit you could predict with 100% accuracy how far the other variable would increase. A perfect negative correlation would indicate a 100% accurate prediction of the decrease in the other variable. If there is no correlation, or a neutral correlation between two variables then changing one variable will have no predictable result on the other variable.

50. DIFFERENTIATE PEARSON PRODUCT MOMENT CORRELATION FROM SPEARMAN RHO COEFFICIENT OF CORRELATION.

The Pearson product-moment correlation coefficient (or Pearson correlation coefficient, for short) is a measure of the strength of a linear association between two variables and is denoted by r. Basically, a Pearson product-moment correlation attempts to draw a line of best fit through the data of two variables, and the Pearson correlation coefficient, r, indicates how far away all these data points are to this line of best fit (i.e., how well the data points fit this new model/line of best fit).

The Spearman rank-order correlation coefficient (Spearman’s correlation, for short) is a nonparametric measure of the strength and direction of association that exists between two variables measured on at least an ordinal scale. It is denoted by the symbols (or the Greek letter ρ, pronounced rho). The test is used for either ordinal variables or for continuous data that has failed the assumptions necessary for conducting the Pearson's product-moment correlation. For example, you could use a Spearman’s correlation to understand whether there is an association between exam performance and time spent revising; whether there is an association between depression and length of unemployment; and so forth.

51. WHEN DO WE USE PEARSON CORRELATION AND SPEARMAN RHO CORRELATION?

For example, you might use a Pearson correlation to evaluate whether increases in temperature at your production facility are associated with decreasing thickness of your chocolate coating. The Spearman correlation evaluates the monotonic relationship between two continuous or ordinal variables.