# What is the inter quartile range of the given data set?

## What is the inter quartile range of the given data set?

The interquartile range is the difference between the third quartile and the first quartile in a data set, giving the middle 50%. The interquartile range is a measure of spread; it’s used to build box plots, determine normal distributions and as a way to determine outliers.

## How do you find quartile range?

Steps:

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 formula of quartile?

When the set of observations are arranged in ascending order the quartiles are represented as, First Quartile(Q1) = ((n + 1)/4)th Term. Second Quartile(Q2) = ((n + 1)/2)th Term. Third Quartile(Q3) = (3(n + 1)/4)th Term.

### How do you find the upper and lower quartiles of an odd number?

If n is odd, include the median value in both halves. Then the lower quartile is the median of the bottom half and the upper quartile is the median of the top half. As an example, if S5 = (1, 2, 3, 4, 5), then the inclusive lower half is (1, 2, 3) and hence Q1 = 2.

### How do you find Q1 with even numbers?

Q1 is the middle value in the first half of the data set. Since there are an even number of data points in the first half of the data set, the middle value is the average of the two middle values; that is, Q1 = (3 + 4)/2 or Q1 = 3.5.

How do you find the upper and lower 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.

## How do you find the interquartile range of grouped data?

The interquartile range formula for grouped data is the same as with non-grouped data, with IQR being equal to the value of the first quartile subtracted from the value of the third quartile.

## Which is the third quartile of the interquartile range?

The third quartile, denoted Q 3, is the value in the data set that holds 25% of the values above it. The quartiles can be determined following the same approach that we used to determine the median, but we now consider each half of the data set separately. The interquartile range is defined as follows:

How to find the interquartile range of a set of data?

To identify the interquartile range of a set of data, simply subtract the first quartile from the third quartile as follows: IQR = Q 3 – Q 1. Where Q 1 is the first, or lower quartile, and Q 3 is the third, or upper quartile.

### When do you use the interquartile range ( IQR )?

InterQuartile Range (IQR) When a data set has outliers or extreme values, we summarize a typical value using the median as opposed to the mean. When a data set has outliers, variability is often summarized by a statistic called the interquartile range, which is the difference between the first and third quartiles.

### Do you include median in quartile range calculator?

If the size of the data set is odd, do not include the median when finding the first and third quartiles. If the size of the data set is even, the median is the average of the middle 2 values in the data set. Add those 2 values, and then divide by 2.