⚠️ Example not found

This example does not exist or may have been moved.

📋

Descriptive

Descriptive Statistics — Exam Scores

Calculate mean, median, standard deviation, and standard error for a sample of 10 exam scores. Covers central tendency, spread, and APA-7 reporting.

📊 M = 79.50, SD = 8.37, Mdn = 80.00

Exam Scores: Central Tendency & Spread

Descriptive

Research Question: A professor records exam scores for 10 students. Describe the distribution.

Student	1	2	3	4	5	6	7	8	9	10
Score	72	85	90	68	78	92	75	88	65	82

1

Mean (x̄):
$\bar{x} = \frac{\sum x_{i}}{n} = \frac{72 + 85 + 90 + 68 + 78 + 92 + 75 + 88 + 65 + 82}{10} = \frac{795}{10} = 79.5$
2

Sample Standard Deviation:
$s = \sqrt{\frac{\sum (x_{i} - \bar{x})^{2}}{n - 1}} = \sqrt{\frac{(- 7.5)^{2} + \dots + (2.5)^{2}}{9}} = \sqrt{\frac{630.5}{9}} = \sqrt{70.06} \approx 8.37$
3

Median (sorted: 65,68,72,75,78,82,85,88,90,92):
$Median = \frac{x_{(5)} + x_{(6)}}{2} = \frac{78 + 82}{2} = 80.0$
4

Standard Error of the Mean:
$S E = \frac{s}{\sqrt{n}} = \frac{8.37}{\sqrt{10}} = \frac{8.37}{3.162} = 2.65$

79.5

Mean

80.0

Median

8.37

2.65

65–92

Range

APA-7

Descriptive statistics for exam scores (N = 10): M = 79.50, SD = 8.37, Mdn = 80.00, range = [65, 92].