4. Find the median, mode, and range for the following lists of data. а. 23, 28, 22, 31, 23 b. -2, 5, 11, -8, 5, -2

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### Question 4
**Find the median, mode, and range for the following lists of data.**

- a. 23, 28, 22, 31, 23
- b. -2, 5, 11, -8, 5, -2

### Explanation and Step-by-Step Solutions

#### Part (a)
**Given List of Data:** 23, 28, 22, 31, 23

1. **Arrange the Data in Ascending Order:**
   22, 23, 23, 28, 31

2. **Median:** The median is the middle value of the ordered list.
   - List: 22, 23, 23, 28, 31
   - Median: 23

3. **Mode:** The mode is the value that appears most frequently in the list.
   - In this list, 23 appears twice.
   - Mode: 23

4. **Range:** The range is the difference between the highest and the lowest values in the list.
   - Highest Value: 31
   - Lowest Value: 22
   - Range: \(31 - 22 = 9\)

#### Part (b)
**Given List of Data:** -2, 5, 11, -8, 5, -2

1. **Arrange the Data in Ascending Order:**
   -8, -2, -2, 5, 5, 11

2. **Median:** The median is the middle value of the ordered list. When there is an even number of values, the median is the average of the two middle numbers.
   - List: -8, -2, -2, 5, 5, 11
   - Median: \(\frac{-2 + 5}{2} = \frac{3}{2} = 1.5\)

3. **Mode:** The mode is the value that appears most frequently in the list.
   - In this list, both -2 and 5 appear twice.
   - Mode: -2 and 5

4. **Range:** The range is the difference between the highest and lowest values in the list.
   - Highest Value: 11
   - Lowest Value: -8
   - Range: \(11 - (-8) = 11 + 8 = 19\)
Transcribed Image Text:### Question 4 **Find the median, mode, and range for the following lists of data.** - a. 23, 28, 22, 31, 23 - b. -2, 5, 11, -8, 5, -2 ### Explanation and Step-by-Step Solutions #### Part (a) **Given List of Data:** 23, 28, 22, 31, 23 1. **Arrange the Data in Ascending Order:** 22, 23, 23, 28, 31 2. **Median:** The median is the middle value of the ordered list. - List: 22, 23, 23, 28, 31 - Median: 23 3. **Mode:** The mode is the value that appears most frequently in the list. - In this list, 23 appears twice. - Mode: 23 4. **Range:** The range is the difference between the highest and the lowest values in the list. - Highest Value: 31 - Lowest Value: 22 - Range: \(31 - 22 = 9\) #### Part (b) **Given List of Data:** -2, 5, 11, -8, 5, -2 1. **Arrange the Data in Ascending Order:** -8, -2, -2, 5, 5, 11 2. **Median:** The median is the middle value of the ordered list. When there is an even number of values, the median is the average of the two middle numbers. - List: -8, -2, -2, 5, 5, 11 - Median: \(\frac{-2 + 5}{2} = \frac{3}{2} = 1.5\) 3. **Mode:** The mode is the value that appears most frequently in the list. - In this list, both -2 and 5 appear twice. - Mode: -2 and 5 4. **Range:** The range is the difference between the highest and lowest values in the list. - Highest Value: 11 - Lowest Value: -8 - Range: \(11 - (-8) = 11 + 8 = 19\)
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