Last night, everyone at the school music concert wrote their age on a slip of paper and placed it in a box. Today, each of the students in a math class selected a random sample of size 10 from the box of papers. Here is a dot plot showing their sample means, rounded to the nearest year.

<p>A dot plot for “sample mean age.” The numbers 31 through 42 are indicated. The data are as follows: 31 years old, 3 dots. 32 years old, 3 dots. 33 years old, 3 dots. 34 years old, 2 dots. 35 years old, 4 dots. 36 years old, 3 dots. 37 years old, 2 dots. 38 years old, 1 dot. 39 years old, 2 dots. 42 years old, 2 dots.</p>  

1. Does the number of dots on the dot plot tell us how many people were at the concert or how many students are in the math class?

2. The mean age for the population is 35 years. If Elena picks a new sample of size 10 from this population, should she expect her sample mean to be within 1 year of the population mean? Explain your reasoning.

3. What could Elena do to select a random sample that is more likely to have a sample mean within 1 year of the population mean?

Andre would like to estimate the mean number of books the students at his school read over the summer break. He has a list of the names of all the students at the school, but he doesn’t have time to ask every student how many books they read.

What should Andre do to estimate the mean number of books?

The lengths in feet of a random sample of 20 male and 20 female humpback whales were measured and used to create the box plot.

Two box plots, male and female. From 38 to 56 by 2's. Male box plot is: whisker from just above 39 to 43. Box from 43 to 46 with vertical line at 44 point 5. Whisker from 46 to 48. Female box plot is: whisker from just above 48 to 49. Box from 49 to just under 52 with vertical line at about 50 point 8. Whisker from 50 point 8 to 54 point 5.  

Estimate the median lengths of male and female humpback whales based on these samples.

Put these numbers in order from least to greatest.

• \(\frac{1}{2}\)
• \(\frac{1}{3}\)
• \(\frac{2}{5}\)
• 0.6
• 0.3