Following are final exam scores, arranged in increasing order, for students in an introductory statistics course.

56

56

58

60

61

61

62

65

70

71

73

75

76

77

78

81

82

83

83

85

87

88

90

92

94

95

97

98

98

Part: **0 / 2**

0 of 2 Parts Complete

Part 1 of 2

(a)Find the first quartile of the scores.

The first quartile of the scores is .

To find the first quartile (Q1) of the scores, you need to follow these steps:

1. **Arrange the data in increasing order**: The scores are already arranged in increasing order.
   
2. **Determine the position of the first quartile**: 
   - The first quartile (Q1) is the 25th percentile of the data.
   - The formula to find the position \( P \) of Q1 in an ordered data set is:
     \[
     P = \frac{n+1}{4}
     \]
     where \( n \) is the number of data points.

3. **Calculate the position**:
   - Here, \( n = 29 \).
   - So, \( P = \frac{29+1}{4} = \frac{30}{4} = 7.5 \).

4. **Interpret the position**:
   - Since 7.5 is not an integer, the first quartile will be the average of the 7th and 8th data points.

5. **Find the 7th and 8th data points**:
   - The 7th data point is 62, and the 8th data point is 65.

6. **Calculate Q1**:
   \[
   Q1 = \frac{62 + 65}{2} = \frac{127}{2} = 63.5
   \]

Thus, the first quartile (Q1) of the scores is **63.5**.

Would you like more details or have any questions? Here are some related questions to expand your understanding:

1. How do you find the third quartile (Q3) for this data set?
2. What is the median of this data set?
3. How would you calculate the interquartile range (IQR) for these scores?
4. How does the presence of repeated scores affect the quartile calculations?
5. What is the difference between a quartile and a percentile?

**Tip:** Remember that the quartiles divide the data into four equal parts, with Q1 and Q3 representing the boundaries of the middle 50% of the data.

Learn how to find the first quartile (Q1) of a set of introductory statistics scores. Follow a step-by-step explanation with a detailed example of calculating Q1 using the position formula. Suitable for high school students studying statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation