Let Us Discover 57 This Simplified Self-learning Module (SSLM) will help you understand the different measures of position of a given set of ungrouped data, the quartiles, deciles, and percentiles. To illustrate these three different measures of position is by understanding their concepts. Measure of position - is a method by which the position that a particular data value has within a given data set can be identified. Quartiles - are the score points which divide a distribution (arranged in ascending order into four equal parts, with one-fourth or 25% of the data values in each part. The 25% from left of the distribution are below the first quartile (Q:) - lower quartile the 50% are below the second quartile (Qa) also known as the median of the distribution, and the 75% are below the third quartile (Qs) - upper quartile. To find Q2 or the median position of the data set, divide the total number of data values (n) by 2 If there are an even number of data values, the median is the value that is the average of the value in the position and the + 1 position. If there are an odd number of data values, the median is the value in the position. For example, if the data set has 20 values such as 25 3 5 7 11 13 17 3 8 12 21 3 14 23 9 20 21 4 6 5 GSC-CID-LRMS-ESSLM... 02.00. Effective April 21, 2021 First, we arrange the distribution in ascending order. . Q: 02 Q. 3 3 3 4 5 5 6 7 8 9 11 12 13 14 17 20 21 21 23 25 3 7 9 11 TT TT 5th 6th 107 11 15 16 Positions Positions Positions In the data set above with 20 values, the median is the average of the data values in 10 and 11" positions. That is the average of 9 and 11, which is 10. Since the median is also the Q therefore Q2 = 10. The first quartile is the median of the first half of the data set and marks the point at which 25% of the data values are lower and 75% are higher. The third quartile is the median of the second half of the data set and marks the point at which 25% of the data values are higher and 75% lower. In the data set above, there are ten data values in each halt, so the first quartile is the average of the values in the fifth and sixth positions. Both of which are 5, so the first quartile or Q1 = 5 and the third quartile is the average of the values in the fifteenth and sixteenth positions 17 and 20 respectively, so the third quartile or Q3 = 18.5. Deciles - are the nine score points which divide a distribution into ten equal parts. Using the above example, 3 3 3 4 5 5 6 7 8 9 11 12 13 14 17 20 21 21 23 25 D1 D D DA D D. Di D Di D. The 1st decile, or D. is the point that has 10% of the observations below it, D has 20% of the observations below it, Da has 30% of the observations falling below it, and so on. In the above example, D:= 3, D2 = 4 D = 5, De = 7. Ds = 9. Do = 12. D+ = 14 D = 20, D. 21 Percentiles - are the ninety-nine score points which divide a distribution into one hundred equal parts. Using the same example, 3 3 3 4 5 5 6 7 8 9 11 12 13 14 17 20 21 21 23 25 t + + t + t t D D. Ds D4 D. De D D. D Pig Pao P PS Peo Pro Poe P The first decile is the 10 percentile (Pro). It means 10% of the data is less than or equal to the value of P10 or D and so on. In our example above P1 = 3, P2 = 4 and so on as the arrow indicated. GSC-CID-LRMS-ESSLM. T. 02.00. Effective April 21, 2021