Quartiles and Percentiles

Q1 is equal to

the median of the lower half of the data set

Q3 is equal to

the median of the upper half of the data set

You take a test and your score ranks among the 80th percentile. How did 20% of test-takers score compare to you?

20% of test-takers scored the same as or higher than you. (You scored worse than 20% of students who took the test)

Q1 is the same as the ______ percentile

25th percentile

How does 30% of the entire data compare to the data point at the 70th percentile?

30% of the entire data is greater than or equal to the data point

Q2 is the same as the _______ percentile

50th percentile (the median)

How does 70% of the entire data compare to the data point at the 70th percentile?

70% of the entire data is less than or equal to the data point

Q3 is the same as the _______ percentile

75th percentile

You take a test and your score ranks among the 80th percentile. How did 80% of test-takers score compare to you?

80% of test-takers scored the same as or less than you. (You scored better than 80% of students who took the test)

IQR (interquartile range)

Q3 - Q1

minimum

The lowest value in a data set

Quartiles

Values that divide a data set into four equal parts

find the percentile rank of x (x = a data value)

[(number of values below x)/total number of data values] x 100

Q1 (First Quartile)

separates the bottom 25% of sorted values from the top 75%

Q2 (Second Quartile)

separates the bottom 50% from the top 50%

The 64th percentile separates

separates the bottom 64% from the top 36% (100% - 64% = 36%)

The 70th percentile is the data point that separates...

separates the bottom 70% from the top 30%

Q3 (Third Quartile)

separates the bottom 75% of sorted values from the top 25%.

the median of a set with an even number of values is...

the average of the middle 2 numbers

maximum

the highest value in a data set

Q2 is equal to

the median

find what data value exists at the 25th percentile

value = (25/100)(number of data values + 1) If the answer is NOT a whole number, round it down to the nearest whole # AND round it up to the nearest whole #. (ex. 5.56 rounds down to 5 and rounds up to 6) Find what the data values are at those positions in the set. (ex. find the 5th data value and the 6th data value.) Average them. (The 5th data value is 5. The 6th data value is 5. The average is 5. That is the answer).

percentiles

values that divide the data into 100 equal parts