Question

There are 276 students.
158 of the students are females.
82 of the males enrolled in magic college.
102 of the females enrolled in magic college.

(a) Create the two-way table based on the given data.
(b) What percentage of students were males that went to magic college?
(c) What percentage of females went to magic college?

Answer 1

Step-by-step explanation:

Number of males is

• 276 - 158 = 118

Number of males not enrolled

• 118 - 82 = 36

Number of females not enrolled

• 158 - 102 = 56

(a)

The table based on data is

                Enrolled        Not enrolled      Total  

Male            82                  36                     118    

Female        102                56                     158  

Total            184                 92                     276

(b)

Percentage of students were males that went to magic college

• enrolled male / total students =           (use table above)
• 82/276*100% = 29.71% (rounded)

(c)

Percentage of females went to magic college

• enrolled female / total female =           (use table above)
• 102/158*100% = 64.56% (rounded)

Answer 2

Answer:

a)  see below

b)  29.7%  (1 d.p.)

c)  64.6%  (1 d.p.)

Step-by-step explanation:

Part (a)

Using the given information to create a two-way table:

$\begin{array}{|l|c|c|c|}\cline{1-4} & \sf Female & \sf Male & \sf Totals\\\cline{1-4} \sf Enrolled & 102 & 82 & \\\cline{1-4} \sf Not\:enrolled & & &\\\cline{1-4} \sf Totals & 158 & & 278\\\cline{1-4}\end{array}$

Calculations to fill the table:

• Total enrolled = 102 + 82 = 184
• Female not enrolled = 158 - 102 = 56
• Male total = 278 - 158 = 120
• Male not enrolled = 120 - 82 = 38
• Total not enrolled = 56 + 38 = 94

Therefore:

$\begin{array}{|l|c|c|c|}\cline{1-4} & \sf Female & \sf Male & \sf Totals\\\cline{1-4} \sf Enrolled & 102 & 82 & 184 \\\cline{1-4} \sf Not\:enrolled & 56 & 38& 94 \\\cline{1-4} \sf Totals & 158 &120 & 278\\\cline{1-4}\end{array}$

Part (b)

$\sf Percentage=\left(\dfrac{Value}{Total\:value}\right) \times 100$

Number of students who are male and enrolled = 82

Total number of students = 278

$\begin{aligned} \implies \sf Percentage\:students\:enrolled & = \sf\left(\dfrac{82}{278}\right) \times 100\\& = \sf 29.7\%\:\:(1\:d.p.) \end{aligned}$

Part (c)

Total number of females enrolled = 102

Total number of females = 158

$\begin{aligned} \implies \sf Percentage\:students\:enrolled & = \sf\left(\dfrac{102}{158}\right) \times 100\\& = \sf 64.6\%\:\:(1\:d.p.) \end{aligned}$