Question

Can you help Jorge organize the results into a two-way frequency table?

Answer 1

See Explanation

Explanation:

Given

Students = 24

Musical Instrument and Sport = 6

Neither = 3

Sport = 14

Required

Complete the two-way frequency table

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------------------

Does not play a musical instrument -------------------------------------3-----------

Total ---------------------------------------------------- 14 ---------------------------------------

To solve this, we'll make use of the following naming rules

A represent students that plays musical instrument; A = 6

B represent students that do not play musical instrument

C represent students that plays sport

D represent students that do not play sport; D = 3

Considering the first column [Plays a sport] and taking note of the naming rules;

`A + B = 14`

Substitute 6 for A

`6 + B = 14`

Solve for B

`B = 14 - 6`

`B = 8`

Also, given that there are 24 students in the class and 14 of them play sport; this implies that 10 do not play sport

Considering the second column [Does not play a sport]

`C + D = 10`

Substitute 3 for D

`C + 3 = 10`

Solve for C

`C = 10 - 3`

`C = 7`

Hence, the complete table is:

-------------------------------------------------------- Plays sport || Does not play sport

Plays a musical instrument ---------------------6--------------------------7----------

Does not play a musical instrument ---------8--------------------------3---------

Total ---------------------------------------------------- 14 -----------------------10---------