Learning Outcomes

Recognize, describe, and also calculate the procedures of place of data: quartiles and also percentiles.

You are watching: The second quartile is the same as the median.


The typical measures of ar are quartiles and also percentiles.

Quartiles space special percentiles. The first quartile, Q_1, is the exact same as the 25th percentile, and also the third quartile, Q_3, is the very same as the 75th percentile. The median, M, is dubbed both the second quartile and the 50th percentile.

The following video clip gives an development to Median, Quartiles and also Interquartile Range, the topic girlfriend will discover in this section.

To calculation quartiles and also percentiles, the data need to be bespeak from the smallest to largest. Quartiles division ordered data right into quarters. Percentiles divide ordered data into hundredths. Come score in the 90th percentile the an exam does no mean, necessarily, the you got 90% top top a test. It means that 90% of test scores room the very same or less than your score and also 10% of the check scores space the very same or greater than her test score.

Percentiles are valuable for compare values. For this reason, universities and also colleges use percentiles extensively. One instance in which colleges and also universities usage percentiles is as soon as SAT outcomes are supplied to recognize a minimum testing score that will be used as an accept factor. Because that example, suppose fight it out accepts sat scores at or above the 75th percentile. The translates right into a score that at least 1220.

Percentiles are mainly used with very huge populations. Therefore, if you to be to say that 90% the the check scores are less (and not the exact same or less) 보다 your score, it would certainly be acceptable since removing one certain data value is not significant.

The median is a number that procedures the “center” of the data. You deserve to think that the typical as the “middle value,” yet it does no actually need to be one of the observed values. It is a number that separates ordered data into halves. Half the values space the exact same number or smaller sized than the median, and half the values are the very same number or larger. For example, consider the adhering to data.

1; 11.5; 6; 7.2; 4; 8; 9; 10; 6.8; 8.3; 2; 2; 10; 1

Ordered from the smallest to largest:

1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5

Since there space 14 observations, the average is in between the seventh value, 6.8, and also the eighth value, 7.2. To find the median, include the 2 values together and divide by two.

displaystylefrac6.8+7.22=7The average is seven. Fifty percent of the worths are smaller sized than seven and fifty percent of the values are larger than seven.

Quartiles room numbers that different the data into quarters. Quartiles might or may not be part of the data. To discover the quartiles, first find the typical or second quartile. The first quartile, Q_1, is the middle value that the lower fifty percent of the data, and also the third quartile, Q_3, is the center value, or median, the the upper half of the data. To obtain the idea, consider the same data set:

1; 1; 2; 2; 4; 6; 6.8; 7.2; 8; 8.3; 9; 10; 10; 11.5

The mean or second quartile is seven. The lower fifty percent of the data space 1, 1, 2, 2, 4, 6, 6.8. The center value of the lower half is two.

1; 1; 2; 2; 4; 6; 6.8

The number two, i beg your pardon is component of the data, is the first quartile. One-fourth that the whole sets of values are the same as or less than two and three-fourths of the values are an ext than two.

The upper fifty percent of the data is 7.2, 8, 8.3, 9, 10, 10, 11.5. The center value the the upper fifty percent is nine.

The third quartile, Q_3, is nine. Three-fourths (75%) the the notified data set are less than nine. One-fourth (25%) of the bespeak data set are greater than nine. The 3rd quartile is part of the data collection in this example.

The interquartile range is a number that suggests the spread out of the middle half or the middle 50% that the data. That is the difference between the 3rd quartile (Q_3) and the an initial quartile (Q_1).

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IQR = Q_3 – Q_1

The IQR can help to identify potential outliers. A value is doubt to it is in a potential outlier if that is much less than (1.5)(IQR) listed below the first quartile or more than (1.5)(IQR) over the third quartile. Potential outliers constantly require more investigation.