How do you calculate the range and interquartile range from the data set containing the values 10, 20, 12, 17, and 16?

Calculating the Range and Interquartile Range

To compute the range and the interquartile range (IQR) of a data set, follow these steps:

Step 1: Organize the Data

First, arrange the data values in ascending order. For your data set:

10, 12, 16, 17, 20

Step 2: Calculate the Range

The range is the difference between the maximum and minimum values in the data set. In this case:

  • Minimum Value = 10
  • Maximum Value = 20

Thus, the range is calculated as follows:

Range = Maximum Value - Minimum Value = 20 - 10 = 10

Step 3: Calculate the Interquartile Range (IQR)

The IQR measures the spread of the middle 50% of the data. To find the IQR, we need to determine the first quartile (Q1) and the third quartile (Q3).

Finding Q1 and Q3:

For a data set of 5 values:

  • Q1 is the median of the first half of the data (below the median)
  • Q3 is the median of the second half of the data (above the median)

Given the ordered data set:

10, 12, 16, 17, 20

The median (Q2) is 16, which is the middle value. Now, identify Q1 and Q3:

  • First half (Q1): 10, 12
    Q1 = (10 + 12) / 2 = 11
  • Second half (Q3): 17, 20
    Q3 = (17 + 20) / 2 = 18.5

Now, calculate the IQR:

IQR = Q3 - Q1 = 18.5 - 11 = 7.5

Final Results

In summary, for the data values of 10, 20, 12, 17, and 16:

  • Range = 10
  • Interquartile Range (IQR) = 7.5

Leave a Comment