Calculate the interquartile range of the following data. Remember that Desmos (right-click and open in new tab/window) can be used to help you calculate some of this.

Question

{35, 20, 41, 48, 79, 83, 83, 97, 120}

(6 points)
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Q1=
Response area

Q3=
Response area

IQR = Response area

Values lower than Response area and higher than Response area are considered outliers.

The outlier in this data set is Response area.

Answer 1

To calculate the interquartile range (IQR) and identify the outlier for the provided data set {35, 20, 41, 48, 79, 83, 83, 97, 120}, we'll follow these steps:

1. Order the data set:
   {20, 35, 41, 48, 79, 83, 83, 97, 120}

2. Calculate Q1 (the first quartile):
   Q1 is the median of the first half of the data. The first half is {20, 35, 41, 48}.
   Median of this half = (35 + 41)/2 = 38

3. Calculate Q3 (the third quartile):
   Q3 is the median of the second half of the data. The second half is {79, 83, 83, 97, 120}.
   Median of this half = 83 (since there's an odd number of data points in this segment)

4. Calculate IQR (Interquartile Range):
   IQR = Q3 - Q1 = 83 - 38 = 45

5. Determine outliers:
   We calculate the fences to find outliers:

   • Lower fence = Q1 - 1.5 * IQR = 38 - 1.5 * 45 = 38 - 67.5 = -29.5
   • Upper fence = Q3 + 1.5 * IQR = 83 + 1.5 * 45 = 83 + 67.5 = 150.5

   Any value below the lower fence or above the upper fence is considered an outlier.
   In this dataset, the only value greater than the upper fence is 120, so:

6. Final Values:

   • Q1 = 38
   • Q3 = 83
   • IQR = 45
   • Outlier = 120

Now we can provide the answers to the input fields:

Q1 = 38
Q3 = 83
IQR = 45
The outlier in this data set is 120.