Faded examples · Calculating frequency density

Calculator

Each example shows a little less than the one before – complete the faded steps yourself, using the same two steps every time: work out the class width, then divide the frequency by it. Also answer the check question.

①Example 1fully worked: read it through

A class $10

1Class width $=$ upper $-$ lower

width $=15-10=5$

2Frequency density $=$ frequency $\div$ width

$\text{FD}=\dfrac{12}{5}=2.4$

Check · What is the class width here?

A $15$B $5$C $10$D $12$

②Example 2fully worked: read it through

A class $0

1Class width $=$ upper $-$ lower

width $=20-0=20$

2Frequency density $=$ frequency $\div$ width

$\text{FD}=\dfrac{30}{20}=1.5$

Check · Why can the frequency ($30$) be more than the frequency density ($1.5$)?

A a mistake – they should be equalB the density is spread over a width of $20$, so per unit it is smallC density is always biggerD frequency is always $1.5$

③Example 3you finish the last 1 step

A class $20

1Class width $=$ upper $-$ lower

width $=32-20=12$

2Frequency density $=$ frequency $\div$ width

$\text{FD}=\dfrac{18}{12}=1.5$

Check · What is $18\div12$?

A $1.5$B $6$C $2.4$D $0.67$

④Example 4your turn: every step

A class $5

1Class width $=$ upper $-$ lower

width $=12-5=7$

2Frequency density $=$ frequency $\div$ width

$\text{FD}=\dfrac{21}{7}=3$

Check · To go back from this bar to the frequency you would...

A multiply the density by the class widthB divide againC add the widthD square the density

Answers · Histograms

Faded examples · Calculating frequency density

① Example 1 width $=15-10=5$→$\text{FD}=\dfrac{12}{5}=2.4$ $2.4$

Check: B: $5$

② Example 2 width $=20-0=20$→$\text{FD}=\dfrac{30}{20}=1.5$ $1.5$

Check: B: the density is spread over a width of $20$, so per unit it is small

③ Example 3 width $=32-20=12$→$\text{FD}=\dfrac{18}{12}=1.5$ $1.5$

Check: A: $1.5$

④ Example 4 width $=12-5=7$→$\text{FD}=\dfrac{21}{7}=3$ $3$

Check: A: multiply the density by the class width