MAS183 Statistical Data Analysis

Mean: 131.16

Median: 97

Standard deviation: 78.95

Tasman Sea

Mean: 67.68

Median: 64

Standard deviation: 33.29

1. c) From the boxplots and the histograms for the length of the rivers flowing into Tasman Sea and Pacific ocean, it can be seen that the distribution of length of rivers flowing into Pacific ocean are is not normally distributed. This is indicated by the median line being below the middle mark of the boxplot. The distribution can be seen to be skewed to the left. The histogram has a long tail to the right. To add on, the distribution of length of rivers flowing into Tasman Sea is almost normally distributed but not perfect. This is indicated by the median and mean values which are almost equal. The line on the boxplot is also slightly above the middle level of the boxplot indicating closeness to normal distribution.
2. d) Both the rivers have got outlier values as there are data points showing above the maximum limit.
3. e) The range being closer to Tasman Sea than Pacific Ocean means that the rivers flowing from the range to Tasman will generally be shorter than the rivers flowing from the range to Pacific Ocean. This can be confirmed by the mean length of the rivers flowing to the two water bodies (Tasman Sea: mean length = 67.67km, Pacific Ocean: mean length = 131.16 km).
4. f) Variable classification(i)

(ii)

(iii)

2. b) Scatterplot
3. c) From the scatterplot above, it can be observed that there is a linear relationship between metacarpal bone length and stature. The relationship is strong and in the positive direction.
4. d) It cannot be the least square line of best fit since it implies that when the length of the metacarpal is less than about 2mm, the length of stature becomes negative yet length can never be negative.
5. e) Equation of least squares line of best fit
6. f) Persons height when metacarpal length is 43mm

= 73.1 + 94.43 = 167.53 cm

1. g) The R² value obtained is 0.73. This means that 73% of the variation that occurs in standing height (stature) is explained by metacarpal length.