Stat 10, UCLA
Chapter 4 Solutions

    1. Average=50, SD=5.
    2. 48, 50, 50 are within 0.5 SDs of average, that is, they fall in the range 47.5-52.5. 48,50,50,54,57 are within 1.5 SDs of the average, that is, in the range 42.5-57.5.

    1. list (ii) has the smaller SD. (3 more entries at the average)
    2. list (i) (two more extreme values)

    1. 5, because only three of the numbers are smaller than 1, and none are bigger than 10.
    2. 3, because if the SD is 1, then the entries 0.6 and 9.9 are much too far away from the average; the SD can't be 6 because none of the numbers are more than 6 away from the average.

  1. income: average would be higher education: median would be higher
    1. (i) 60 (ii) 50 (iii) 40
    2. (i) median is bigger than average -- long left hand tail (ii) median is about equal to the average -- symmetry (iii) median is less than the average -- long right had tail
    3. 15, because most of the area is within 50 of the average, so 50 is too big; and only a small portion of the area is within 5 of the average, so 5 is too small.
    4. False. The two histograms are almost mirror images and have about the same SD. (Remember the rule for what happens to the SD when changing the sign of a list of numbers.)

    1. Average weight of men = 66*2.2 = (about) 145 pounds. SD = (about) 20 pounds. Average weight of women = (about) 121 pounds. SD = (about) 20 pounds.
    2. 68%. Then range is from one SD below the average to one SD above.
    3. Bigger than 9kg. When you combine the men and women together, the spread increases.

    1. No. Girls must be taller than boys
    2. 141cm

    1. 163. Guess the average!
    2. 68%. Then range is from one SD below the average to one SD above.
    3. $8 (the SD=$8)