13. Frequency Table

Question 1

The following table shows the number of goals scored by a football team over the course of 30 games.

Find the mean number of goals scored over the 30 games.

Give your answer to 1 decimal place.

Select the correct answer from the list below:

A: 2.2goals

B: 1.9goals

C: 2.7goals

D: 3.1goals

CORRECT ANSWER:  

WORKED SOLUTION:

Mean number of goals,

(0\times3)+(1\times7)+(2\times6)+(3\times10)+(4\times4)=65

65\div30=2.2goals

Level 4

Question 2

The following table shows the number of goals scored by a football team over the course of 30 games.

The same football team enter a 10 match tournament.

Use the table to estimable the number of times the team scored 2 goals in one game.

Select the correct answer from the list below:

A: 5

B: 1

C: 3

D: 2

CORRECT ANSWER:  D: 2

WORKED SOLUTION:

0.2\times 10=2times

Level 4

Question 3

Use the frequency table below to find the mean number of coats owned by the class.

Give your answer to 3 significant figures.

Select the correct answer from the list below:

A: 2

B: 2.3

C: 0.435

D: 47

CORRECT ANSWER:   A: 2

WORKED SOLUTION:

To find the mean we need to multiply the number of coats owned by the frequencies, add them, then divide by the total frequency. This is most easily done by adding another column and row.

Now that we have the total number of coats owned and the total frequency, we just need to divide them.

\dfrac{46}{23}=2

Level 4

Question 4

The table below shows the number of rain coats owned by students in a class.

What is the modal number of coats owned?

Select the correct answer from the list below:

A: 3 coats

B:  1 coat

C:  2 coats

D:  1.6 coats

CORRECT ANSWER:   B:  1 coat

WORKED SOLUTION:

Select the value that occurs most often.

Level 4

Question 5

The number of pairs of shoes owned by a class of 40 students has been collected and summarised in the frequency table below.

However, some of the data has been lost.

The mean of the data is 2.9.

Use this information to determine the missing frequencies in the table.

What is the modal number of coats owned?

Select the correct answer from the list below:

A: 3 coats

B:  1 coat

C:  2 coats

D:  1.6 coats

CORRECT ANSWER:   B:  1 coat

WORKED SOLUTION:

Letting frequency of one pair of shoes, be x, and the frequency of three pairs of shoes be, y, we can set up the equations,

\begin{aligned} \dfrac {(1 \times x) +(2 \times 12) + (3 \times y) + (4 \times 8) + (5 \times 3)}{40}& = 2.9 \\ \dfrac {x + 24 + 3y + 32 + 15}{40} & = 2.9 \\  \dfrac {x + 3y + 71}{40} &= 2.9 \\ x+3y +71 & = 116 \\ x+3y & = 45 \end{aligned}

and

\begin{aligned} x + 12 + y + 8 + 3 & = 40 \\ x+y +23 & =40 \\ x+y & = 17 \end{aligned}

Here we now have two simultaneous equations that we can solve.

 x+3y  = 45 and  x+y  = 17

If subtract the second equation from the first we are left with,

\begin{aligned} (x + 3y) - (x+y) &= 45 -17 \\ 2y & = 28 \\ y & =14 \end{aligned}

Substituting this value back into the second equation,

\begin{aligned} x+y & = 17 \\ x+14 &= 17 \\ x &=3 \end{aligned}