Question

Question 1 2 marks Consider the data set below. 7.8, 4.9, 5.1, 6.0. 4.6, 4.4. 5.3, 5.1.5.1 (a) [0.5 mark] Find the mean of the data set above. You may use your calculator, but you muast show enough work to demonstrate your process (b) [0.5 mark] Find the median of the data set above. You may use your caleulator, but you must show enough work to demonstrate your process )1 mark] Find the variance of the data set above. You may use your calculator, but you must show enough work to demonstrate your process

Answer 1

A Mean

$Mean=\frac{\sum_{i=1}^{n}x_{i}}{n}=\frac{7.8+4.9+5.1+6+4.6+4.4+5.3+5.1+5.1}{9}=\frac{48.3}{9}=5.367$

median

Arrange observation in ascending order

4.4 4.6 4.9 5.1 5.1 5.1 5.3 6.0 7.8

Total ovservations are 9 hence middle observation is 5th observation which is 5.1

Hence median is 5.1

Variance

$Variance=\frac{\sum_{i=1}^{n}(x-\bar{x})^2}{n-1}=\frac{\sum_{i=1}^{n}(x-5.367)^2}{8}=1.035$