IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability-Sampling Techniques
Topic :Static and Probability- Weightage : 21 %
All Questions for Topic : Sampling techniques,Data manipulation and misinterpretation,Graphical representations (including: bivariate graphs, scatter graphs, box plots, cumulative frequency graphs)
,Lines of best fit,Data processing: quartiles and percentiles,Measures of dispersion: interquartile range,Correlation, qualitative handling,Relative frequency,Response rates,Sets, including notation and operations up to three sets,Probability with Venn diagrams, tree diagrams and sample spaces,Mutually exclusive events,Combined events
Question (23 marks)
The following video shows how mathematics can be used to make predictions for population growth over time and space.
Use the table in Tab 1 below to answer questions (a), (b) and (c).
The table below shows the age distribution of the population of Australia (percentage to nearest $1 \%$, data correct as at 2015).
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Question (a) : 1 marks
Write down the modal class for the age distribution in Australia.
▶️Answer/Explanation
Ans:
To determine the modal class for the age distribution in Australia, we need to identify the age group with the highest percentage.
From the given table, we can see that the highest percentage is $32\%$, which corresponds to the age group $20<A\leq 40$.
Therefore, the modal class for the age distribution in Australia is $20<A\leq 40$.
Question (b) : 1 marks
Show that the estimated mean age is $38.2$
▶️Answer/Explanation
Ans:
To calculate the estimated mean age, we need to find the midpoint of each age group and multiply it by its corresponding percentage. Then, we sum up these products to get the estimated mean age.
Let’s calculate the estimated mean age using the given table:
Age Group 1: $0 < A \leq 20$
Midpoint: $10$
Percentage: $23\%$
Age Group 2: $20 < A \leq 40$
Midpoint: $30$
Percentage: $32\%$
Age Group 3: $40 < A \leq 60$
Midpoint: $50$
Percentage: $27\%$
Age Group 4: $60 < A \leq 80$
Midpoint: $70$
Percentage: $17\%$
Age Group 5: $80 < A \leq 100$
Midpoint: $90$
Percentage: $1\%$
Now, let’s calculate the estimated mean age:
$\text{Estimated Mean Age} = (10 \times 23\%) + (30 \times 32\%) + (50 \times 27\%) + (70 \times 17\%) + (90 \times 1\%)$
Calculating the values:
$\text{Estimated Mean Age} = (2.3) + (9.6) + (13.5) + (11.9) + (0.9) = 38.2$
Therefore, the estimated mean age is 38.2.