Questions and Answers

IB Math Studies Statistics

1. IB Mathematical Studies SL – Statistics, Types of Variables

How can I identify what kind of variable is the number of tails when 4 coins are tossed?

Solution

IB Mathematical Studies SL – Statistics, Types of Variables

The result of an experiment like this one could be 0,1,2,3 or 4 times of seeing tails. Therefore this variable represents quantitative discrete data.

2. IB Mathematical Studies SL – Statistics, Types of Variables

How can I identify what kind of variable represents the players’ height of a basketball team?

Solution

IB Mathematical Studies SL – Statistics, Types of Variables

The height is numerical data which takes positive values within a reasonable interval. So, it is a quantitative continuous data.

3. IB Mathematical Studies SL – Statistics, Mean value

How can I find the mean of the following data set?

2,3,6,1,2,3,5,2,3

Solution

IB Mathematical Studies SL – Statistics, Mean value

The mean of a data set values is their arithmetic average.

$\bar{x}=\frac{2+3+6+1+2+3+5+2+3}{9}=\frac{27}{9}=3$

4. IB Mathematical Studies SL – Statistics, Mode

How can I find the mode of the following data set?

2,7,6,1,2,7,5,4,7

Solution

IB Mathematical Studies SL – Statistics, Mode

The mode(s) of a data set values is this (these) value (s) which occurs most frequently.

Concerning this question, the mode is the value 7 since occurs most frequently (3 times).

5. IB Mathematical Studies SL – Statistics, Median

How can I find the median of the following data set?

2,7,6,1,2,7,5,4,7

Solution

IB Mathematical Studies SL – Statistics, median

The median of dataset values is the middle value after they have been placed in increasing order. If the number of values is even then the median is the average between the two mid values.

If the dataset contains an odd number of values, k say, the median value is the $( \frac{k+1}{2})th$ value, while the dataset contains an even number of values, k say, the median value is the average of the $( \frac{k}{2})th$ and $( \frac{k}{2}+1)th$ values.

The dataset in increasing order will be

1,2,2,4,5,6,7,7,7

We observe that the mid value of this dataset is 5. So the median is 5.

6. IB Mathematical Studies SL – Statistics, Median

How can I find the median of the following data set?

2,7,6,1,2,7,5,4,7, 8

Solution

IB Mathematical Studies SL – Statistics, median

The median of dataset values is the middle value after they have been placed in increasing order. If the number of values is even then the median is the average between the two mid values.

The dataset in increasing order will be

1,2,2,4,5,6,7,7,7,8

We observe that the mid values of this dataset are 5 and 6. So the median is their average,

i.e. $median=\frac{5+6}{2}=\frac{11}{2}=5.5$