St Leonard’s College
GENERAL MATHEMATICS 2012
Application Task
Name:
Teacher:
Male and female heights in different countries
The study of height is known as auxology. Growth and height have long been recognised as the measure of the
health and wellness of individuals. Adult heights between ethnic groups often differ significantly and the average
height for each sex within a country's population is significantly different.
The average height (mean) of males and females in 100 countries are shown on Data Sheet 1. The heights are in
cm.
Our investigation aims are to:

Examine the heights of males from particular countries

Compare the heights of males and females in the group

Determine what type of relationship exists between male heights and female heights

Test whether the male height is a good predictor of a female’s height
G.M. Statistics Analysis Task 2012
Name: ___________________________________
Part A (37 marks)
In this section you will analyse male and female heights from different countries.
A1. Randomly select 20 countries from Data Sheet 1 and record the male and female heights in the
table below.
No.
Country
Male
Height
(cm)
Female
Height
(cm)
No.
Country
Male
Height
(cm)
Female
Height
(cm)
[2 marks]
Use your selected sample to answer the questions in Part A and Part B.
Page 2 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
A2 a. Using the class intervals shown in the table, complete the frequency distribution table and
construct a histogram for the heights of males from your sample of 20 countries. Label the axes
clearly.
Height (cm)
tally
frequency
Cumulative
frequency
𝟏𝟒𝟎 − < 150
𝟏𝟓𝟎 − < 160
𝟏𝟔𝟎 − < 170
𝟏𝟕𝟎 − < 180
𝟏𝟖𝟎 − < 190
[3 marks]
Histogram
[3 marks]
b. What is the modal class.
Page 3 of 10
[1 mark]
G.M. Statistics Analysis Task 2012
Name: ___________________________________
c. Describe the shape of the distribution of male heights in your sample.
[1 mark]
d. Calculate the percentage of male students in your sample (to the nearest whole number) who had
a height of 170 cm or greater.
[2 marks]
e. Using the data in the frequency distribution table construct a cumulative frequency curve (ogive)
for the male heights. Label the axes clearly.
[4 marks]
f. Using the cumulative frequency curve work out the number of males who had a height less than
175cm. Indicate on your graph how you obtained this value and state this value in the space below.
[2 marks]
Page 4 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
g. Convert the value you found in part f to a percentage of males with a height less than 175cm.
[2 marks]
A3. Calculate the mean, standard deviation and 5 Number Summary Statistics for the male and
female heights, giving your answers correct to 2 decimal places.
Statistic
Male Height
Female Height
Mean
Standard deviation
Min Height
Lower Quartile
Median
Upper Quartile
Max Height
[4 marks]
A4 a. Draw scaled and labelled parallel box plots for the Male Heights and Female Heights data.
Heights in cm
[7 marks]
Page 5 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
b. Describe the shape of each distribution of the data displayed in the box plots.
[2 marks]
A5 a. Compare the centre of heights for both males and females in your sample. What do the
measures of the centre illustrate for your sample? Quote relevant statistics to support your
statements.
b. Compare the spread of heights for both males and females in your sample. What do the measures
of the spread illustrate for your sample? Quote relevant statistics to support your statements.
[2+2=4 marks]
Page 6 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
Part B (26 marks)
B1. In this section we are aiming to determine if the male height is a good predictor of the female
height. Write down the independent variable.
[1 mark]
B2. Construct a scatter plot of the data that you selected in A1, making sure you place the
independent variable on the horizontal axis.
Use an appropriate scale on both axes and label the axes clearly.
[4 marks]
B3. By observing the scatterplot ONLY, describe the apparent relationship between the variables in
terms of strength, direction and form.
[3 marks]
B4 a. Determine the value of Pearson's correlation coefficient, 𝑟, to 4 decimal places.
𝑟 = __________________________
Page 7 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
b. Using the scatter plot in B1 and this r value, comment on the relationship between the male and
female heights.
c. Find the coefficient of determination,𝑟 2 , to 4 decimal places.
𝑟 2 =______________________________
d. Interpret 𝑟 2 in terms of the female and male heights.
[1 + 2 + 1 + 2 = 6 marks]
B5 a. Determine the least squares regression line for the data. Round your coefficients to 4 decimal
places.
female height = _______________ × male height + _____________
b. Using the least squares regression equation, predict the female height when the male height is
165cm. Give the answer to 1 decimal place.
Page 8 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
c. Using the least squares regression equation, predict the female height when the male height is
185 cm. Give the answer to 1 decimal place.
d. Using the data from B5b and B5c above, accurately plot the two points on the scatter plot,
labelling the points A and B. Draw a line through the two points.
e. Comment on the reliability of your predictions in B5b and B5c.
[2 + 1 + 1 + 2 + 2 = 8 marks]
B6. Interpret the gradient of the least squares regression line in terms of the variables.
[2 marks]
B7. Consider a female who has a height of 150cm. Predict the height of a male using the equation
found in B5. a
[2 marks]
Page 9 of 10
G.M. Statistics Analysis Task 2012
Name: ___________________________________
Section C – Conclusion
Reread the introduction to the task. What discoveries have been made in relation to the aims of the
investigation? Quote relevant statistics where appropriate.
(approximately 100 words)
[3 marks[
[Total = 66 marks]
ACCURACY: (correct rounding of numbers and use of specified number of decimal places) [2 marks]
Total marks = 68
Page 10 of 10