Question

the dot plot shows the survey results of 9 members of the latinx club, including elias and valeria. each member surveyed a random sample of 50 students in the school. what can valeria use instead of her survey result to make a better inference about the population? the mean of the survey results which is the best estimate of the percentage of students at the school who speak spanish at home? 21% 36% 42% 48%

Explanation:

Step1: Calculate the total number of students who speak Spanish at home from the dot - plot

From the dot - plot, we count the number of dots for each value:

• For \(x = 18\): \(1\) dot
• For \(x=20\): \(2\) dots
• For \(x = 21\): \(3\) dots
• For \(x=22\): \(2\) dots
• For \(x = 24\): \(1\) dot

The total number of students who speak Spanish at home in the samples is \(1\times18+2\times20 + 3\times21+2\times22+1\times24\)

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Since each member surveyed \(n = 50\) students and there are \(N=9\) members, the total number of surveyed students is \(50\times9=450\)

Step2: Calculate the percentage

The percentage \(P\) is given by the formula \(P=\frac{\text{Total number of students who speak Spanish at home}}{\text{Total number of surveyed students}}\times100\%\)

Substitute the values: \(P=\frac{189}{450}\times 100\%\)

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Answer:

\(42\%\)