What Do Quartiles Tell Us?

Quartiles tell us about the spread of a data set by breaking the data set into quarters, just like the median breaks it in half.This means that when we calculate the quartiles, we take the sum of the two scores around each quartile and then half them (hence Q1= (45 + 45) ÷ 2 = 45) .

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What does the first quartile tell us about data?

Each quarter is 25% of the total number of data points. The first quartile or Q1 is the value in the data set such that 25% of the data points are less than this value and 75% of the data set is greater than this value.

How do you interpret and find the quartiles?

How to Calculate Quartiles

  1. Order your data set from lowest to highest values.
  2. Find the median. This is the second quartile Q2.
  3. At Q2 split the ordered data set into two halves.
  4. The lower quartile Q1 is the median of the lower half of the data.
  5. The upper quartile Q3 is the median of the upper half of the data.

What quartile deviation tells us?

The semi interquartile range (SIR) (also called the quartile deviation) is a measure of spread. It tells you something about how data is dispersed around a central point (usually the mean). The SIR is half of the interquartile range.

What does Q1 and Q3 mean?

Q1 is the median (the middle) of the lower half of the data, and Q3 is the median (the middle) of the upper half of the data. (3, 5, 7, 8, 9), | (11, 15, 16, 20, 21). Q1 = 7 and Q3 = 16.

What does the third quartile tell us about data?

Quartiles Summary
How? Well, the median tells us the center of the data set, while the first and third quartiles tell us about how spread out the middle 50% of the data set is. Finally, the minimum and maximum values tells us about the most extreme values in the data set.

How do you interpret interquartile range?

The interquartile range (IQR) is the distance between the first quartile (Q1) and the third quartile (Q3). 50% of the data are within this range. For this ordered data, the interquartile range is 8 (17.5–9.5 = 8). That is, the middle 50% of the data is between 9.5 and 17.5.

How do you interpret quartile decile and percentile?

Quartiles: distribution is divided into quarters. Quintiles: distribution is divided into fifths. Deciles: distribution is divided into tenths. Percentile: distribution is divided into hundredths.

What is the value of median?

Median: To find the median of a data set, arrange the data values in order. from least to greatest or greatest to least; the median is the data value in the middle; if there is an even number of data values in the set, the median is the mean of the two middle values.

How do you find quartiles in statistics?

The formula for quartiles is given by:

  1. Lower Quartile (Q1) = (N+1) * 1 / 4.
  2. Middle Quartile (Q2) = (N+1) * 2 / 4.
  3. Upper Quartile (Q3 )= (N+1) * 3 / 4.
  4. Interquartile Range = Q3 – Q1.

Is quartile a measure of dispersion?

Quartile deviation is an absolute measure of dispersion. The relative measure corresponding to this measure, called the coefficient of quartile deviation is calculated as follows: Coefficient of quartile deviation can be used to compare the degree of variation in different distributions.

What are the uses of quartile and standard deviation?

ft is a simple measure of dispersion. QD is most relevant to find out the dispersion of the distribution when the measure of central tendency is taken as median. QD is more useful than range because QD speaks about the 50% of the scores of a distribution, while range speaks about the highest and lowest scores.

What is quartile deviation Slideshare?

Quartile Deviation: Definition The quartile deviation is half of the difference between first quartile (Q1) and third quartile (Q3). This is also known as quartile coefficient of dispersion.

What is third quartile example?

An Example
In other words, the median is: (7 + 8)/2 = 7.5. Here the median is (15 + 15)/2 = 15. Thus the third quartile Q3 = 15.

How do you find Q1 Q2 and Q3 in statistics?

Quartile Formula:

  1. Formula for Lower quartile (Q1) = N + 1 multiplied by (1) divided by (4)
  2. Formula for Middle quartile (Q2) = N + 1 multiplied by (2) divided by (4)
  3. Formula for Upper quartile (Q3) = N + 1 multiplied by (3) divided by (4)
  4. Formula for Interquartile range = Q3 (upper quartile) – Q1 (lower quartile)

What is the value of the third quartile?

The third quartile (or upper quartile), Q3, has an f-value equal to 0.75. The interquartile range, IQR, is defined as Q3-Q1.

Why is interquartile range important?

The Significance of the Interquartile Range
The range gives us a measurement of how spread out the entirety of our data set is. The interquartile range, which tells us how far apart the first and third quartile are, indicates how spread out the middle 50% of our set of data is.

What does the range tell us about our data?

In statistics, the range is the spread of your data from the lowest to the highest value in the distribution.The range is calculated by subtracting the lowest value from the highest value. While a large range means high variability, a small range means low variability in a distribution.

Is it better to have a higher or lower interquartile range?

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.

How do you interpret 3rd decile?

Let’s calculate the 3rd decile:

  1. D3 = Value of 3 (30 + 1) / 10.
  2. D3 = Value of 9.3rd position, which is 0.3 between the scores of 65 and 66.
  3. Thus, D3 = 65 + 1 (0.3) = 65.3.
  4. 30% of the 30 scores in the observation fall below 65.3.

What is the relationship between quartiles and percentiles?

The percentiles and quartiles are related in the sense that, the lower quartile (Q1) equals the 25th percentile, the middle quartile (Q2) equal to the 50th percentile, while the upper quartile (Q3) equals the 75th percentile.