Victory for the ACT Student Text 15e

L ESSON 6 | S TATISTICS , P ROBABILITY , AND D ATA R EPRESENTATION • 249

LESSON 6 Statistics, Probability, and Data Representation

MEASURES OF CENTER

1. If the average of 35, 38, 41, 43, and x

is 37,

3. The average of 10 test scores is 80. If the high and low scores are dropped, the average is 81. What is the average of the high and low scores? A. 76 B. 78 C. 80 D. 81 E. 82  ƒ–‹ ͳͲͳǡ –Š‡ ϐ‹ƒŽ ‡šƒ ‰”ƒ†‡ ‹• weighted two times as heavily as the mid-term grade. If Leo received a score ‘ˆ ͺͶ ‘ Š‹• ϐ‹ƒŽ ‡šƒ ƒ† ͻͲ ‘ Š‹• mid-term, what was his course average? F. 88 G. 87.5 H. 86.5 J. 86 K. 85 4.

what is x ? A. 28 B. 30 C. 31 D. 34 E. 36

Throwback to Math Class Here are the steps –‘ ϐ‹† ƒ missing element of an average: 1. Multiply the average by the total number of quantities. 2. Add together the known quantities. 3. Subtract the result of Step 2 from the result of Step 1.

2. The average weight of 6 packages is 50 pounds per package. Another package is added, making the average weight of the 7 packages 52 pounds per package. What is the weight, in pounds, of the additional package? F. 2 G. 7 H. 52 J. 62 K. 64

The Cambridge Edge When computing weighted averages, don’t check your calculations, but do check that: 1. The average weights the components properly. 2. The correct number of quantities is used.

The Cambridge Edge For item #1, instead of working with the given values, work with the “aboves” and the “belows.” There are three numbers above the average: 38 (1 above), 41 (4 above), and 43 (6 above). There is one number below: 35 (2 below). These two groups need to balance. Right now, the above group totals 11 above the average and the below group totals 2 below, so we need to add a value to the below ‰”‘—’ –Šƒ– ‹• ͻ „‡Ž‘™ –Š‡ ƒ˜‡”ƒ‰‡ǡ –‘ „ƒŽƒ…‡ –Š‡ –™‘ ‰”‘—’•Ǥ ˆ –Š‹• •‡‡• –‘‘…‘’Ž‹…ƒ–‡†ǡ Œ—•– —•‡ –Š‡ ϐ‹”•– ’ƒ”– ‘ˆ –Š‡ •–”ƒ–‡‰›Ǥ Clearly we need a number less than 37 in the “belows” group. And it probably needs to be less than 36 or 34. This helps you quickly eliminate a few choices without doing any math.