IB myp 4-5 MATHEMATICS – Practice Questions- All Topics
Topic :Static and Probability–Correlation, qualitative handling
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 (a) : 2 marks
The number of employees in the office building each day is given in the table below.
Find the mean number of employees in the office building during the working days.
▶️Answer/Explanation
Ans:
To calculate the mean number of employees using LaTeX formula, we can use the following formula:
\[
\text{{Mean}} = \frac{{\sum \text{{Number of employees}}}}{{\text{{Number of working days}}}}
\]
In this case, the sum of the number of employees is $105 + 70 + 90 + 75 + 60 = 400$, and the number of working days is 5.
Plugging these values into the formula, we get:
\[
\text{{Mean}} = \frac{{400}}{{5}} = 80
\]
Hence, the mean number of employees in the office building during the working days is 80.
Question (b) : 2 marks
To control the temperature in the office building, a central air-conditioning unit is needed. The power $(\mathrm{P})$ of the air-conditioning unit is measured in horsepower (hp) and can be found using the following formula:
$$
P=\frac{(\rm{6 V+500} \mathrm{~N})}{9000}
$$
Where:
$\mathrm{V}$ is the volume in cubic feet.
$\mathrm{N}$ is the mean number of employees during the working days.
Using your answers from part (a) and part (b), determine the value of $\mathrm{P}$ needed for controlling the temperature in this office building.
▶️Answer/Explanation
Ans:
To determine the value of \( P \) (power) needed for controlling the temperature in the office building, we can substitute the given values into the formula:
\[ P = \frac{{6V + 500N}}{{9000}} \]
where \( V = 39000 \) ft\(^3\) (volume) and \( N = 80 \) (mean number of employees).
Substituting the values:
\[ P = \frac{{6 \times 39000 + 500 \times 80}}{{9000}} \]
\[ P = \frac{{234000 + 40000}}{{9000}} \]
\[ P = \frac{{274000}}{{9000}} \]
\[ P \approx 30.44 \]
Therefore, the value of \( P \) needed for controlling the temperature in this office building is approximately 30.44 horsepower (hp).