Exam 1

1. Metainformation

   Tag	Value
   file	Descriptive-statistics_eur-descriptive-113-en_eur-descriptive-113-en
   name	eur-descriptive-113-en
   section	Descriptive statistics/Summary Statistics/Measures of Spread/Standard Deviation
   type	num
   solution	0.45
   tolerance	0
   Type	Calculate
   Program	Calculater
   Language	English
   Level	Statistical Literacy

   Question

   On the first question in the exam of course 2.8, 189 students gave a correct answer and 71 students gave an incorrect answer. Suppose we create a variable based on the scores for this exam question, where 0 = incorrect answer and 1 = correct answer.

   What is the standard deviation of this variable?

   
   

   Solution

   The standard deviation of this variable is $\sqrt{p \times (1 - p)}$, where $p$ is the proportion correct: $\frac{189}{189+71}= .73$. Thus, the standard deviation is $\sqrt{.73 \times (1 - .73)} = .45$ (taking the square root of the variance).