Pren recorded this data set, which contains an outlier:

[tex]$204, 216, 111, 224, 230, 211, 210, 198, 200, 218$[/tex]

What numbers represent the range, lower quartile, and upper quartile?

A. Range: 210.5, Lower Quartile: 200, Upper Quartile: 218
B. Range: 14, Lower Quartile: 111, Upper Quartile: 198
C. Range: 119, Lower Quartile: 218, Upper Quartile: 200
D. Range: 119, Lower Quartile: 200, Upper Quartile: 218

First, we start by arranging the data in increasing order. The given data set is

[tex]$$204,\;216,\;111,\;224,\;230,\;211,\;210,\;198,\;200,\;218.$$[/tex]

When sorted, the data becomes

[tex]$$111,\;198,\;200,\;204,\;210,\;211,\;216,\;218,\;224,\;230.$$[/tex]

Step 1. Calculate the Range

The range is defined as the difference between the maximum and minimum values. Here, the minimum value is [tex]$111$[/tex] and the maximum value is [tex]$230$[/tex]. Thus,

[tex]$$\text{Range} = 230 - 111 = 119.$$[/tex]

Step 2. Determine the Lower Quartile [tex]$(Q_1)$[/tex]

Since there are [tex]$10$[/tex] numbers, we divide the data set into two halves of [tex]$5$[/tex] numbers each to determine the quartiles.

The lower half of the data is:

[tex]$$111,\;198,\;200,\;204,\;210.$$[/tex]

The median of this lower half is the third number (since there are [tex]$5$[/tex] numbers), which is

[tex]$$Q_1 = 200.$$[/tex]

Step 3. Determine the Upper Quartile [tex]$(Q_3)$[/tex]

The upper half of the data is:

[tex]$$211,\;216,\;218,\;224,\;230.$$[/tex]

The median of this upper half is the third number, which is

[tex]$$Q_3 = 218.$$[/tex]

Final Answer:

- Range: [tex]$119$[/tex]
- Lower Quartile: [tex]$200$[/tex]
- Upper Quartile: [tex]$218$[/tex]