Question 1176521: Compute for the quartiles,Interquartile,And Range each set of ungrouped data
A.Math scores in science:22,41,39,16,20,18,23,37,34,26,36,27,25,20
B.Number of Hours spent in using social media in a week by grade 10 students:
111,130,128,105,109,107,112,126,123,115,128
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! Absolutely! Let's compute the quartiles, interquartile range (IQR), and range for each dataset.
**A. Math Scores in Science:**
1. **Arrange the data in ascending order:**
16, 18, 20, 20, 22, 23, 25, 26, 27, 34, 36, 37, 39, 41
2. **Find the quartiles:**
* **Q1 (First Quartile):** The median of the lower half of the data. Since there are 14 data points, the lower half contains the first 7 values. The median of these values is the average of 20 and 22, which is 21.
* **Q2 (Second Quartile/Median):** The median of the entire dataset. The median is the average of 25 and 26, which is 25.5.
* **Q3 (Third Quartile):** The median of the upper half of the data. The upper half contains the last 7 values. The median of these values is the average of 36 and 37, which is 36.5.
3. **Calculate the Interquartile Range (IQR):**
* IQR = Q3 - Q1 = 36.5 - 21 = 15.5
4. **Calculate the Range:**
* Range = Maximum value - Minimum value = 41 - 16 = 25
**Results for Math Scores:**
* Q1: 21
* Q2 (Median): 25.5
* Q3: 36.5
* IQR: 15.5
* Range: 25
**B. Number of Hours Spent Using Social Media:**
1. **Arrange the data in ascending order:**
105, 107, 109, 111, 112, 115, 123, 126, 128, 128, 130
2. **Find the quartiles:**
* **Q1 (First Quartile):** The median of the lower half of the data. Since there are 11 data points, the lower half contains the first 5 values. The median of these values is 109.
* **Q2 (Second Quartile/Median):** The median of the entire dataset, which is 115.
* **Q3 (Third Quartile):** The median of the upper half of the data. The upper half contains the last 5 values. The median of these values is 128.
3. **Calculate the Interquartile Range (IQR):**
* IQR = Q3 - Q1 = 128 - 109 = 19
4. **Calculate the Range:**
* Range = Maximum value - Minimum value = 130 - 105 = 25
**Results for Social Media Hours:**
* Q1: 109
* Q2 (Median): 115
* Q3: 128
* IQR: 19
* Range: 25
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