what is the mathematical definition of lower quartile?
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A quartile is a type of quantile which divides the number of data points into four more or less equal parts, or quarters. ... It is also known as the lower quartile or the 25th empirical quartile and it marks where 25% of the data is below or to the left of it (if data is ordered on a timeline from smallest to largest).
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Percentile. A percentile is a value on a scale of one hundred that indicates the percent of a distribution that is equal to or below it. ... A 50th percentile is the same as a "median." An average, or "mean," is similar but a weighted result.
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Less than is one of the terms used to show the relationship between two values. It states that one value is lesser than the other. The sign for less than is < and with this metric, we can compare numbers, weights, heights, and values. For example, there are 4 marbles in one Bowl A, and 7 marbles in Bowl B.
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The interquartile range is often used to find outliers in data. Outliers here are defined as observations that fall below Q1 − 1.5 IQR or above Q3 + 1.5 IQR.
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The 50th percentile is generally the median (if you're using the third definition—see below). The 75th percentile is also called the third quartile. The difference between the third and first quartiles is the interquartile range.
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A high z -score means a very low probability of data above this z -score. ... Note that if z -score rises further, area under the curve fall and probability reduces further. A low z -score means a very low probability of data below this z -score. The figure below shows the probability of z -score below −2.5 .
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It is also called the 75th percentile. The interquartile range (IQR) is the difference between the upper (Q3) and lower (Q1) quartiles, and describes the middle 50% of values when ordered from lowest to highest. The IQR is often seen as a better measure of spread than the range as it is not affected by outliers.
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In a set of data, the quartiles are the values that divide the data into four equal parts. The median of a set of data separates the set in half. ... The interquartile range or IQR is the range of the middle half of a set of data. It is the difference between the upper quartile and the lower quartile.
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Quartiles divide data into quarters. The first quartile (Q1) is the 25th percentile,the second quartile (Q2 or median) is 50th percentile, and the third quartile (Q3) is the the 75th percentile.
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The difference between the first and third quartiles, called the interquartile range, shows how the data is arranged about the median. A small interquartile range indicates data that is clumped about the median. A larger interquartile range shows that the data is more spread out.
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The Excel QUARTILE function returns the quartile (each of four equal groups) for a given set of data. QUARTILE can return minimum value, first quartile, second quartile, third quartile, and max value. array - A reference containing data to analyze. quart - The quartile value to return.
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['quartile.', 'quartier.', 'quartern.', 'quartans.', 'quartics.', 'quartets.', 'quarters.', 'quartzes.']
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The QUARTILE. ... The difference between these two functions is that QUARTILE. INC bases its calculation on a percentile range of 0 to 1 inclusive, whereas QUARTILE. EXC bases its calculation on a percentile range of 0 to 1 exclusive.
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['Order the data from least to greatest.', 'Find the median.', 'Calculate the median of both the lower and upper half of the data.', 'The IQR is the difference between the upper and lower medians.']
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Explanation : Quartile is not a measure of dispersion because it is the measure of central tendency. ... Only range, mean deviation, standard deviation are the measure of dispersion.
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If there are (4n+3) data points, then the lower quartile is 75% of the (n+1)th data value plus 25% of the (n+2)th data value; the upper quartile is 25% of the (3n+2)th data point plus 75% of the (3n+3)th data point.
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The 25th percentile is also known as the first quartile (Q1), the 50th percentile as the median or second quartile (Q2), and the 75th percentile as the third quartile (Q3). In general, percentiles and quartiles are specific types of quantiles.