Pictograms and tally charts (age 11+)

Question 1

A researcher wants to estimate the average height of all 7th‑grade students at Lincoln Middle School. She measures the heights of 30 students who are on the school’s basketball team. Which statement best describes the usefulness of this sample for making an inference about the entire 7th‑grade population?

Accepted Answer

The sample is not likely to be representative because it only includes basketball players, so the estimate may be inaccurate.

Answer

Since the sample size is 30, it is automatically representative of the population.

Answer

If the sample were chosen randomly from all 7th graders, it would guarantee a representative sample.

Answer

A sample must include at least half of the population to be representative.

Question 2

A researcher wants to estimate the average amount of time 7th‑grade students at a school spend on homework each night. She randomly selects 40 students from the entire school and records their homework time. Which statement best describes why she can use the results from her sample to make an inference about all 7th‑grade students at the school?

Accepted Answer

Because the sample was selected randomly, it is likely to be representative of the whole population, allowing a valid generalization.

Answer

Because the sample includes only 40 students, it cannot be used to make any inference about the whole population.

Answer

Because the researcher only needs a few students, any small group will give a reliable estimate of the population.

Answer

Because 40 students is a large number, the sample automatically gives the exact average for all students.

Question 3

Mrs. Lee wants to estimate the percentage of students in her school whose favorite subject is science. She draws three separate random samples, each containing 40 students, and records the percentage who choose science in each sample. Why is it helpful for her to take several random samples of the same size instead of just one?

Accepted Answer

It lets her see how much the sample percentages might vary, giving an idea of the sampling variability.

Answer

It makes the total number of students surveyed larger, which automatically makes the estimate more accurate.

Answer

It guarantees that the average of the three sample percentages will equal the true population percentage.

Answer

It ensures that every student in the school is included in at least one of the samples.

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