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Measure of Position or Location

These measures include standard scores, percentiles, deciles and quartiles which are used to locate the relative position of a data value in a data set. Standard scores tell how many standard deviations a data value is above or below the mean and allow comparison between different tests by converting raw scores into comparable units. Quartiles divide a distribution into four equal groups with Q1 at the 25th percentile, Q2 at the 50th percentile (median), and Q3 at the 75th percentile. Deciles divide a distribution into ten equal groups denoted by D1, D2, etc. Outliers are extremely high or low data values that can strongly affect statistics like the mean and standard deviation.

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354 views2 pages

Measure of Position or Location

These measures include standard scores, percentiles, deciles and quartiles which are used to locate the relative position of a data value in a data set. Standard scores tell how many standard deviations a data value is above or below the mean and allow comparison between different tests by converting raw scores into comparable units. Quartiles divide a distribution into four equal groups with Q1 at the 25th percentile, Q2 at the 50th percentile (median), and Q3 at the 75th percentile. Deciles divide a distribution into ten equal groups denoted by D1, D2, etc. Outliers are extremely high or low data values that can strongly affect statistics like the mean and standard deviation.

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Melvin Cabonegro
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Measure of Position or Location - These measures include standard scores, percentiles, deciles and quartiles.

- They are used to locate the relative position of a data value in the data set. - For example, if a value is located at the 80th percentile, it means that 80% of the values fall below it in the distribution and 20% of the values fall above it. Standard Scores There is a saying, You cant compare apples and oranges. But with the use of statistics, it can be done to some extent. Suppose that a student scored 90 on a music test and 45 on an English exam. Direct comparison of raw scores is impossible, since the exam might not be equivalent in terms of number of questions, value of each question, and so on. However, a comparison of a relative standard similar to both can be made. This comparison uses the mean and standard deviation and is called a standard score or z score. A standard score or z score tells how many standard deviation a data value is above or below the mean for a specific distribution values. If a standard score is zero, then the data is the same as the mean. A z score or standard score for a value is obtained by subtracting the mean from the value and dividing the result by the standard deviation. The symbol for a standard score is z. the formula is

Quartiles and Deciles Quartiles divide the distribution into four groups, separated by Q1, Q2, Q3. Note that Q1 is the same as the 25th percentiles; Q2 is the same as the 50th percentile, or the median; Q3 corresponds to the 75th percentile as shown:

Quartiles can be computed by using the formula for computing percentiles. For Q1 use p = 25. For Q2 use p = 50. For Q3 use p = 75. However, an easier method for finding quartiles is found by in this Procedure Table.

For samples, the formula is

For the population, the formula is Where: z standard score x value / mean s/ standard deviation The z score represents the number of standard deviations that a data value falls above or below the mean. Percentiles - are position measure used in educational and health-related fields to indicate the position of an individual in a group. - Symbolized by P1, P2, P3,., P99 and divide the distribution into 100 groups. Deciles divide the distribution into 10 groups, as shown. They are denoted by D1, D2, etc.

Percentile formula The percentile corresponding to a given values X is computed by using the following formula.

Outliers - An outlier is an extremely high or an extremely low data value with the rest of the data values. - They can strongly affect the mean and standard deviation of a variable. - For example, suppose a researcher mistakenly recorded an extremely high data value. This value would then make the mean and standard deviation of the variable much larger than they really were. - They can have an effect on other statistics as well.

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