Percentiles

Quartiles

4 equal parts

Quintiles

5 equal parts

Sextiles

6 equal parts

Septilies

7 equal parts

Octiles

8 equal parts

uses of percentile

A percentile (rank) is used to determine where a particular score or value fits within a broader distribution. For example: A student receives a score of 75 out of 100 on an exam and wishes to determine how her score compares to the rest of the class. She calculates a percentile rank for a score of 75 based on the reported scores of the entire class.

Percentiles definition

A percentile is a measure that tells us what percent of the total frequency scored at or below that measure.

Finding percentile

Calculate the percentile ? 1 step - arranging the values in ascending order 2 step - Formula (Nearest rank method) P = ( k ÷ 100) (n)

Percentile

derived from Latin word " per centum"- per hundred. - any of the 99 values which divide a sorted data set into 100 equal parts, so that each part represents 1/ 100 of the data set. Is a statistical measure indicating the value at or below which a given percentage of observations in a group of observations fall. Are values in a series of observations arranged in ascending order of magnitude which divide the distributions into 100 equal parts

Percentiles

divide the distribution in to 100 equal parts

Deciles

into 10 equal parts

Finding percentile rank

Formula: To find the percentile rank of a score, X, out of a set of n scores, where X is included: (B + 0.5(E) ) / n x 100

Finding percentile for grouped data

Formula - step 1: find the cumulative frequencies for the distributions of scores step2: multiply the total number of scores in the distribution (n) by the proportion for the 50th percentile (p=0.5). this gives us the ordered rank p(n) of the median score. step3: the interval containing the 50th percentile is the 1st class interval of the cumulative frequency greater than or equal to p(n)=32 step4: find the true lower limit (Y) and the true upper limit (Y) for the class interval containing the 50th percentile. step5: find the interval width (i) for the class interval containing the 50th percentile by subtracting the true limit from the true upper limit. step6: find the number of the scores (f) within the class interval containing the 50th percentile score. step 7: Find the cumulative frequency for the class interval immediately below the class interval containing the 50th percentile (cf ). step 8: Insert these values into the formula for the score at the 50th percentile (Y ) and solve.

Quantiles - measures of position

It is necessary at times, to be able to measure how an item fits into the data, how it compares to other items of the data, or even how it compares to another item in another data set.

50th percentile

The 50 th percentile will have 50 % of the observations on either side. Thus the 50th percentile is the median.

Quartiles -

Three points that divide the data set into four equal groups, each group comprising a quarter of the data. First quartile ( Q1) or the 25th percentile Second quartile (Q2) also called the median or the 50th percentile Third quartile (Q3) or the 75th percentile Interquartile range (IQR) is the difference between the upper and lower quartiles. (IQR = Q3 - Q1)

Quantiles

are cut points dividing the range of a probability distribution into contiguous intervals with equal probabilities .

percentile rank

is the percentage of scores that fall at or below a given score/ value.

Mean , median and mode

measures of central value ( locate the mid point in a distribution)