Ekene was curious if sample range was an unbiased estimator of population range. She placed ping pong balls numbered from 0 to 32 in a drum and mixed them well. Note that the range of the population is 32.
She then took a random sample of 5 balls and calculated the range of the sample. She replaced the balls and
repeated this process for a total of 50 trials. Her results are summarized in the dotplot below, where each dot
represents the sample range from a sample of 5 balls.
.
ea
8
12
16
20
24
28
32
Sample range
Based on these results, does sample range appear to be a biased or unbiased estimator of population range?
Hint: The population range is 32.
Choose 1
Sample range appears to be a biased estimator since it consistently underestimated the population

Write the summation to estimate the area under the curve y = 1 + x2 from x = -1 to x = 2 using 3 rectangles and right endpoints

Item 1 solve for s. s+24=90 −114 −66 66 114

An annual marathon covers a route that has a distance of approximately 26 miles. winning times for this marathon are all over 2 hours. the following data are the minutes over 2 hours for the winning male runners over two periods of 20 years each. earlier period 14 12 15 22 13 10 19 13 9 14 20 18 16 20 23 12 18 17 6 13 recent period 7 11 7 14 8 9 11 14 8 7 9 8 7 9 9 9 9 8 10 8 (a) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the earlier period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks. for more details, view how to split a stem.) minutes beyond 2 hours earlier period 0 1 2 (b) make a stem-and-leaf display for the minutes over 2 hours of the winning times for the recent period. use two lines per stem. (use the tens digit as the stem and the ones digit as the leaf. enter none in any unused answer blanks.) minutes beyond 2 hours recent period (c) compare the two distributions. how many times under 15 minutes are in each distribution