Relative Frequency

a) 12 students out of the total of 52 used public transport so, as a fraction, this can be expressed as:

 

\dfrac{12}{52}

To calculate the relative frequency as a decimal to 3 decimal places, divide the top by the bottom:

 

\dfrac{12}{52}=0.231 to 3 decimal places

 

b) 16 students out of the total of 52 walked to school so, as a fraction, this can be expressed as:

 

\dfrac{16}{52}

 

To calculate the relative frequency as a decimal to 3 decimal places, divide the top by the bottom:

 

\dfrac{16}{52}=0.308 to 3 decimal places

 

c) If 9 of the 52 students cycled, then the number who didn’t cycle is:

 

52-9=43

 

As a fraction, this can be expressed as:

 

\dfrac{43}{52}

 

To calculate the relative frequency as a decimal to 3 decimal places, divide the top by the bottom:

 

\dfrac{43}{52}=0.827 to 3 decimal places

In Bev’s experiment, the relative frequency of rolling a 6 is:

 

\dfrac{63}{400}=0.1575

 

The probability of rolling a 6 is:

 

\dfrac{1}{6}=0.166666...

 

The two results are fairly similar, in fact in Bev’s experiment she has successfully thrown a 6 slightly less often than would be expected, although not by a significant amount.

 

So, we can conclude that Bev’s statement is false.  The die does not appear to be biased.

a) The relative frequency of silver cars  using Hannah’s morning data can be calculated as follows:

 

\dfrac{32}{32+48}=0.4=40\%.

 

So, according to her data, her statement is correct.

 

b) To calculate the relative frequency based on all the data collected, we will need to combine Hannah’s data.

 

The total number of cars spotted was 32 +41 + 48 + 111 = 232\text{ cars}.

The total number of silver cars spotted was 32+41=73\text{ silver cars}

 

The relative frequency of a car being silver using all the data can be calculated as follows:

 

\dfrac{73}{232}=0.315 to 3 decimal places

 

c) To find the expected frequency of silver cars, we will multiply the probability of a car being silver (i.e., the relative frequency calculated in part b) by the total number of cars. The expected frequency of silver cars in the town is therefore:

 

0.315\times5,000=1,575 silver cars

a)  Bob throws the die 100 times and throws a 7 on 15 occasions.  As a fraction this can be written as:

 

\dfrac{15}{100}

 

The probability of Bob throwing a 7 is the decimal equivalent of the above fraction, which we can calculate by dividing the numerator by the denominator:

 

15\div100 = 0.15

 

b)  Susan throws the die 500 times and throws a 7 on 60 occasions.  As a fraction this can be written as:

 

\dfrac{60}{500}

 

The probability of Susan throwing a 7 is the decimal equivalent of the above fraction, which we can calculate by dividing the numerator by the denominator:

 

60\div500 = 0.12

 

c)  Susan’s results are more accurate because the more times you conduct an experiment, the more accurate the estimate will be.

a)  Since the relative frequency for Burger Queen is 0.1, we should be able to turn this into a fraction without too much difficulty:

0.1 = \dfrac{1}{10}

 

We know that 16 people in total opted for Burger Queen, therefore:

 

\frac{1}{10} = 16\text{ students}

 

If 16 students represents \frac{1}{10} of the total number of students, then the total number of students on the trip can be calculated as follows:

 

16\text{ students}\times10 = 160\text{ students}

 

b)  The relative frequency of Pizza Cottage is 0.4 which, as a fraction is \frac{4}{10}.  If there are 160 students in total and \frac{4}{10} chose Pizza Cottage, then the number of students who chose Pizza Cottage can be calculated as follows:

 

 \dfrac{4}{10}\times160\text{ students} = 64\text{ students}

 

c)  The relative frequency of Dazza’s Fish and Chips is 0.5 which, as a fraction is \frac{5}{10} or \frac{1}{2}.  If there are 160 students in total and \frac{1}{2} chose Dazza’s Fish and Chips, then the number of students who chose Dazza’s Fish and Chips can be calculated as follows:

 \dfrac{1}{2}\times160\text{ students} = 80\text{ students}

or

160\text{ students}\div2  = 80\text{ students}