Question

1. Expand the following: a) Σ ( a + b%) where i varies from 1 to n. b) ( Σ up where i varies from 1 to 3. 2a) Define the arithmetic mean, mode, and the median. MeaR b) Consider the following data on grades received by a student in a particular course Weight 25% o 30% .30 45% , Tests Grades Test145 Test 2: 50 Final Exam: 65 Compute the weighted average of grades. 3 a) In 2015, the median total income of households in Greater Sudbury was $71,687 while the mean income was $89,941. Show in a diagram, the likely shape of income distribution with approximate locations of the mean, median, and mode 5 91483

Answer 1

1. A)$\sum$a+b$\sum$x_i

B) ( $\sum$u₁+$\sum$u₂+$\sum$u₃)^2

2. A) Mean: The average of the values. Mathematically it is given as sum of all values divided by number of data points.

Mode: The value that occurs most frequently in the data set.

Median: The central or middle value, separating the top and bottom half after arranging the data in ascending order.

B) Weighted Average= 0.25(45)+ 0.3(50)+ 0.45(65)=55.5

3. The distribution will be right skewed i.e. the peak will be on the left portion of the graph and median value will come before the mean since median is smaller than the mean. The mean is at $89,941 which means that the tail of the distribution i.e. most of the values lie on the right portion of the graph.