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

a) see below

b) 29.7% (1 d.p.)

c) 64.6% (1 d.p.)

Explanation:

Part (a)

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

`\begin{array}\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\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((Value)/(Total\:value)\right) * 100`

Number of students who are male and enrolled = 82

Total number of students = 278

`\begin{aligned} \implies \sf Percentage\:students\:enrolled & = \sf\left((82)/(278)\right) * 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((102)/(158)\right) * 100\\& = \sf 64.6\%\:\:(1\:d.p.) \end{aligned}`

Answer 2

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)