How do you find the interquartile IQR?

The IQR describes the middle 50% of values when ordered from lowest to highest. To find the interquartile range (IQR), ​first find the median (middle value) of the lower and upper half of the data. These values are quartile 1 (Q1) and quartile 3 (Q3). The IQR is the difference between Q3 and Q1.

How do you find the IQR deviation?

We can find the interquartile range or IQR in four simple steps:

  1. Order the data from least to greatest.
  2. Find the median.
  3. Calculate the median of both the lower and upper half of the data.
  4. The IQR is the difference between the upper and lower medians.

How do you find the interquartile mean?

1, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 38. We now have 6 of the 12 observations remaining; next, we calculate the arithmetic mean of these numbers: xIQM = (5 + 6 + 6 + 7 + 7 + 8) / 6 = 6.5. This is the interquartile mean.

What does it mean when IQR is high?

“Feature Films” which has higher IQR than that of “Children’s Film and TV”, so you can say that, it’s more likely that the price for “Feature Films” will vary much as compared to “Children’s Film and TV”.

How do you solve for IQR?


  1. Step 1: Put the numbers in order.
  2. Step 2: Find the median.
  3. Step 3: Place parentheses around the numbers above and below the median. Not necessary statistically, but it makes Q1 and Q3 easier to spot.
  4. Step 4: Find Q1 and Q3.
  5. Step 5: Subtract Q1 from Q3 to find the interquartile range.

What is the IQR rule for outliers?

A commonly used rule says that a data point is an outlier if it is more than 1.5 ⋅ IQR 1.5\cdot \text{IQR} 1. 5⋅IQR1, point, 5, dot, start text, I, Q, R, end text above the third quartile or below the first quartile.

Is the IQR the mean?

The IQR is used to measure how spread out the data points in a set are from the mean of the data set. The higher the IQR, the more spread out the data points; in contrast, the smaller the IQR, the more bunched up the data points are around the mean.

Does higher IQR mean more variability?

The interquartile range is the third quartile (Q3) minus the first quartile (Q1). But the IQR is less affected by outliers: the 2 values come from the middle half of the data set, so they are unlikely to be extreme scores. The IQR gives a consistent measure of variability for skewed as well as normal distributions.

What is the IQR rule?

Using the Interquartile Rule to Find Outliers Multiply the interquartile range (IQR) by 1.5 (a constant used to discern outliers). Add 1.5 x (IQR) to the third quartile. Any number greater than this is a suspected outlier. Subtract 1.5 x (IQR) from the first quartile. Any number less than this is a suspected outlier.

What is IQR in math?

The “Interquartile Range” is the difference between smallest value and the largest value of the middle 50% of a set of data.

What is 1.5 * IQR?

1.5 times the interquartile range is 6. Our fences will be 6 points below Q1 and 6 points above Q3. Any observations less than 2 books or greater than 18 books are outliers. There are 4 outliers: 0, 0, 20, and 25.

Why is 1.5 IQR rule?

Well, as you might have guessed, the number (here 1.5, hereinafter scale) clearly controls the sensitivity of the range and hence the decision rule. A bigger scale would make the outlier(s) to be considered as data point(s) while a smaller one would make some of the data point(s) to be perceived as outlier(s).