Standard deviationIB MYP Maths Extended: Mind map

Exam questions on Standard deviation

1. Five students in Singapore record how many minutes it takes them to solve a puzzle: $4,\ 6,\ 7,\ 9,\ 14$. Use technology and the population standard deviation $\sigma$ where needed.
   A sixth student takes exactly $8$ minutes. State the new mean and find the new standard deviation. Say whether the spread has increased or decreased.2 marks
2. A teacher investigates how the standard deviation changes as values spread out. Each list below has five values and mean $10$. List P is $8,9,10,11,12$ with standard deviation $1.41$. List Q is $6,8,10,12,14$ with standard deviation $2.83$. List R is $4,7,10,13,16$ with standard deviation $4.24$. (All standard deviations are given to 3 significant figures.)
   List T is $5,7.5,10,12.5,15$. Use the pattern to predict its standard deviation, then verify your prediction using technology.2 marks
3. Two courier companies in Nairobi each make five deliveries to the same shop. The delivery times in minutes are: Company X: $20,\ 24,\ 28,\ 32,\ 36$. Company Y: $26,\ 27,\ 28,\ 29,\ 30$.
   Find the mean and the standard deviation of the delivery times for each company.3 marks