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Bivariate Data, SM-Bank 003

Ahmed collected data on the age (`a`) and height (`h`) of males aged 11 to 16 years.

He created a scatterplot of the data and constructed a line of best fit to model the relationship between the age and height of males.
 

  1. Determine the gradient of the line of best fit shown on the graph.   (1 mark)

  2. Determine the equation of the line of best fit shown on the graph.  (2 marks)

  3. Use the line of best fit to predict the height of a typical 17-year-old male.   (1 mark)

  4. Why would this model not be useful for predicting the height of a typical 45-year-old male?   (1 mark)

Show Answers Only
  1. `text(Gradient = 6)`
  2. `h = 6a + 80`
  3. `text(182 cm)`
  4. `text(People slow and eventually stop growing)`

  5.  

    `text(after they become adults.)`

Show Worked Solution

i.    `text{Gradient}\ =(176-146)/(16-11)=30/5=6`
 

ii.   `text{Gradient = 6,  Passes through (11, 146)}`

`y-y_1` `=m(x-x_1)`
`h-146` `=6(a-11)`
`:. h` `=6a-66+146`
  `=6a + 80`
♦♦ Mean marks of 38% and 25% respectively for parts (i)-(ii).
COMMENT: Choose extreme points for calculating gradient.

 
iii.   `text{Substitue}\ \ a=17\ \ \text{into equation from part (ii):}`

`h=(6 xx 17) +80=182`

`:.\ text{A typical 17 year old is expected to be 182cm.}`
  

iv.    `text(People slow and eventually stop growing)`
  `text(after they become adults.)`

Bivariate Data, SM-Bank 001

The graph shows a line of best fit describing the life expectancy of people born between 1900 and 2000.
 


  1. According to the graph, what is the life expectancy of a person born in 1932?  (1 mark)

  2. Determine the value of the gradient of the line of best fit.  (2 marks)

Show Answers Only
  1. \(\text{68 years}\)
  2. \(0.25\)
Show Worked Solution

i.    \(\text{68 years}\)

ii.    \(\text{Using (1900,60), (1980,80):}\)

\(\text{Gradient}\) \(= \dfrac{y_2-y_1}{x_2-x_1}\)
  \(= \dfrac{80-60}{1980-1900}\)
  \(= 0.25\)