Descriptive statistics
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This document discusses various measures of variability and relative position used in descriptive statistics. It defines measures of variability such as range, quartile deviation, variance, and standard deviation, which provide information about the spread or dispersion of values. Measures of relative position, including sigma scores, standard scores, percentiles, and percentile ranks, allow one to compare an individual score to others in a distribution. Standard scores like z-scores, T-scores, and H-scores convert raw scores to derive scores with a standardized mean and standard deviation. Percentiles and percentile ranks divide a scale into 100 equal parts or indicate the percentage of scores below a given score.
Descriptive statistics
- 1. P. MERCY RANI M.Phil Dept.of.education Periyar university Salem-11 DESCRIPTIVE STATISTICS
- 2. Measures of variability Measures of in variability provide formation about the amount of spread or dispersion among the variables. Definitions: dispersion is a measure of the extent to which the individual items vary. - L.R connor dispersion is the measure of the variation of the items. -A.L bowley
- 3. Types of Measures of Variability The researcher to indicate how spread out a group of scores. Range Quartile Deviation variance standard deviation
- 4. The Range: The range is the difference between the largest and smallest values in a set of values. Range = L – S
- 5. QUARTILE DEVIATION: It represents the difference between the third quartile and the first quartile. Quartile Déviation or Q.D = Q3 – Q1 2 MEAN DEVIATION: The mean deviation is also known as the average deviation. It is the average difference between the items in a distribution and the median or mean of that series. M.D. = Σ f | x | N
- 6. Standard Deviation The standard deviation is the square root of variance. σ = √ Σ fx2 N This measure - the average of the squared deviations from the mean is called the variance. σ2 = Σ x2 N
- 7. MEASURES OF RELATIVE POSITIONS Measures of relative position indicate where is score is in relation to all other scores in the distribution. Measures of relative position permit one to express how well an individual has performed as compared to all other individuals in the sample. RAW SCORE A raw score on a test, taken by itself, has no meaning. It gets meaning only by comparison with some reference group or groups. The comparison may be done with help of the following measures.
- 8. 1.Sigma scores 2.Standard scores 3.Percentiles 4.Percentile ranks Sigma scores : Deviation from mean expressed in (σ) terms are called sigma scores The mean of a set of (σ ) scores is always and the standard deviation is always unity The sigma scores are also useful in hypothesis testing determination of percentile ranks and probability judgments.
- 9. STANDARD SCORES OR DERIVED SCORES Provide information about where a score falls in relation to the other scores in the distribution of data A standard score is a measure of relative position which is appropriate when the data represent an interval or ratio scale of measurement. The most commonly reported and used standard scores are T scores or Z scores.
- 10. RAW SCORES: A score is numerically description of an individual’s performance. The numerical outcome of any evaluation done by the help of scale is called Raw Scores. TYPES OF SCORES: For the general analysis and interpretation of data there are 4 types of standard score for the purpose of analysis interpretation of data. These 4 score are 1. Z score 2. z score 3. T score 4. H score
- 11. ‘Z’ SCORE: Z score is also known as (σ) score. Z score may be defined as basic standard score derived from raw scores by help of its different of mean in S.D. “Z “SCORE: The standard score or Z-score involve decimals and directional signs. To avoid this the Z-value is multiplied by 10 and then 50 is added. The new score is called Z-score. It is a type of derived score where mean = 50 and S.D = 10. Z= 10Z +50
- 12. T SCORE: T score is a derived score that is 3rd type of standard score (SS). It is a score which has been developed by MC call. This standard score is internationally used. It is a standard score where mean= 50, SD =10 by the principles of conversion = T score = 10Z+50 H SCORE: This score are developed by Hull. It is an important standard score. It is a score where mean is 50 and standard deviation is always 14. so by the principles of conversion. H=14Z+50
- 13. PERCENTILES: Percentiles the points which divide the entire scale of measurement into 100 equal parts. They are denoted by ( p0, p1, p2,…….,p50,……,p99 ,p100 )
- 14. PERCENTILE RANKS: Score that divides a distribution into 100 equal parts. A percentile ranks indicates the percentage of scores that fall as or below a given score (or) raw score. Percentile ranks help individuals interpret their test scores in comparison to others. PercentileRank (number of data valuesbelow 0.5 the given data point) 100% totalnumber of values