How to Find the Upper Quartile in Statistics: Step-by-Step Guide and Example

The Upper Quartile

The upper quartile (Q3) is a measure of statistical dispersion that divides a dataset into quarters

The upper quartile (Q3) is a measure of statistical dispersion that divides a dataset into quarters. It represents the data point below which 75% of the data lies. In other words, Q3 is the value that separates the highest 25% of the data from the lower 75%.

To find the upper quartile, you need to follow these steps:

1. Organize your dataset in ascending order, from the lowest value to the highest.
2. Calculate the position of Q3 using the formula: Position of Q3 = (3 * n + 1) / 4, where n is the total number of data points in the dataset.
3. If the position of Q3 is an integer, directly find the corresponding value in the dataset at the calculated position. If the position is not an integer, round it down to the nearest whole number. The value at this position is the upper quartile.
4. If the position is a decimal, you can use linear interpolation to estimate the upper quartile. To do this, consider the values at the calculated position and the next position. Interpolate between these two values using the formula: Upper Quartile = Value at the lower position + (Position of Q3 – Lower position) * (Value at the higher position – Value at the lower position).

Let’s understand this with an example:

Consider the following dataset: 12, 15, 18, 22, 24, 26, 27.

1. Organize the dataset in ascending order: 12, 15, 18, 22, 24, 26, 27.
2. Calculate the position of Q3: (3 * 7 + 1) / 4 = 5.
3. As the position of Q3 is an integer, the value at the 5th position is the upper quartile. In this case, it is 24.
4. Therefore, the upper quartile for this dataset is 24.

Remember, the upper quartile is one of the measures used to understand the spread and distribution of data. It is particularly useful when combined with the lower quartile and median to create a box plot, which provides a visual representation of the dataset’s distribution.

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