The raw scores of 20 students of Utopia High School who took part in an examination in Economics are given below. The pass mark is 40% 38 28 70 43 39 20 64 ...

Answer Details

Scores: 38, 28, 70, 43, 39, 20, 64, 66, 12, 46, 52, 53, 20, 34, 48, 69, 18, 20, 64, 34. Number of students \(n = 20\), pass mark = 40%.

(a) Mean score. The sum of all scores is 838.

\[ \bar{x} = \frac{\sum x}{n} = \frac{838}{20} = 41.9 \]

The mean score is 41.9%.

(b) Number who passed. Scores of 40 and above are: 70, 43, 64, 66, 46, 52, 53, 48, 69, 64. That is 10 students.

(c) Percentage who failed. Failures = \(20 - 10 = 10\) students.

\[ \text{Percentage failed} = \frac{10}{20} \times 100 = 50\% \]

(d) Range of scores. Highest = 70, lowest = 12.

\[ \text{Range} = 70 - 12 = 58 \]

(e) Number scoring below the mean (41.9). Scores below 41.9 are: 38, 28, 39, 20, 12, 20, 34, 18, 20, 34, giving 10 students.