Math / Data & Statistics

QuestionQuestion Fill in the following contingency table and find the number of students who both play sports AND play an instrument. \begin{tabular}{|l|l|l|l|} \hline Students & play an instrument & do not play an instrument & Total \\ \hline play sports & & & 51 \\ \hline do not play sports & 23 & & 48 \\ \hline Total & & 46 & \\ \hline \end{tabular}
Provide your answer below:

Studdy Solution

STEP 1

1. The contingency table represents categories of students based on playing sports and playing an instrument.
2. The totals for each row and column must be consistent with the given data.

STEP 2

1. Fill in the missing values in the contingency table.
2. Calculate the number of students who both play sports and play an instrument.

STEP 3

Identify the known values in the table:
- Total students who play sports: 51 - Students who do not play sports and play an instrument: 23 - Total students who do not play sports: 48 - Total students who play an instrument: 46

STEP 4

Calculate the number of students who do not play sports and do not play an instrument:
$\text{Total do not play sports} - \text{Do not play sports and play an instrument} = 48 - 23 = 25$

STEP 5

Calculate the total number of students:
$\text{Total students} = \text{Total play sports} + \text{Total do not play sports} = 51 + 48 = 99$

STEP 6

Calculate the number of students who play sports and play an instrument:
$\text{Total play an instrument} - \text{Do not play sports and play an instrument} = 46 - 23 = 23$

STEP 7

Calculate the number of students who play sports and do not play an instrument:
$\text{Total play sports} - \text{Play sports and play an instrument} = 51 - 23 = 28$

STEP 8

The number of students who both play sports and play an instrument is:
$\boxed{23}$

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Studdy Solution

STEP 1

1. The contingency table represents categories of students based on playing sports and playing an instrument.
2. The totals for each row and column must be consistent with the given data.

STEP 2

1. Fill in the missing values in the contingency table.
2. Calculate the number of students who both play sports and play an instrument.

STEP 3

Identify the known values in the table:
- Total students who play sports: 51 - Students who do not play sports and play an instrument: 23 - Total students who do not play sports: 48 - Total students who play an instrument: 46

STEP 4

Calculate the number of students who do not play sports and do not play an instrument:
$\text{Total do not play sports} - \text{Do not play sports and play an instrument} = 48 - 23 = 25$

STEP 5

Calculate the total number of students:
$\text{Total students} = \text{Total play sports} + \text{Total do not play sports} = 51 + 48 = 99$

STEP 6

Calculate the number of students who play sports and play an instrument:
$\text{Total play an instrument} - \text{Do not play sports and play an instrument} = 46 - 23 = 23$

STEP 7

Calculate the number of students who play sports and do not play an instrument:
$\text{Total play sports} - \text{Play sports and play an instrument} = 51 - 23 = 28$

STEP 8

The number of students who both play sports and play an instrument is:
$\boxed{23}$

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Studdy Solution

STEP 1

1. The contingency table represents categories of students based on playing sports and playing an instrument.2. The totals for each row and column must be consistent with the given data.

STEP 2

1. Fill in the missing values in the contingency table.2. Calculate the number of students who both play sports and play an instrument.

STEP 3

Identify the known values in the table:- Total students who play sports: 51 - Students who do not play sports and play an instrument: 23 - Total students who do not play sports: 48 - Total students who play an instrument: 46

STEP 4

STEP 5

Calculate the total number of students:Total students=Total play sports+Total do not play sports=51+48=99 \text{Total students} = \text{Total play sports} + \text{Total do not play sports} = 51 + 48 = 99 Total students=Total play sports+Total do not play sports=51+48=99

STEP 6

STEP 7

Calculate the number of students who play sports and do not play an instrument:Total play sports−Play sports and play an instrument=51−23=28 \text{Total play sports} - \text{Play sports and play an instrument} = 51 - 23 = 28 Total play sports−Play sports and play an instrument=51−23=28

STEP 8

The number of students who both play sports and play an instrument is:23 \boxed{23} 23​

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1. The contingency table represents categories of students based on playing sports and playing an instrument.
2. The totals for each row and column must be consistent with the given data.

1. Fill in the missing values in the contingency table.
2. Calculate the number of students who both play sports and play an instrument.

Identify the known values in the table:
- Total students who play sports: 51 - Students who do not play sports and play an instrument: 23 - Total students who do not play sports: 48 - Total students who play an instrument: 46

Calculate the total number of students:
$\text{Total students} = \text{Total play sports} + \text{Total do not play sports} = 51 + 48 = 99$

Calculate the number of students who play sports and do not play an instrument:
$\text{Total play sports} - \text{Play sports and play an instrument} = 51 - 23 = 28$

The number of students who both play sports and play an instrument is:
$\boxed{23}$