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### Chapter 3

HW solutions

No. 64

- a. The weights are: 23,19,26,17,21,24,22.
- The mean is 21.71. The median can be found by sorting:
- 17 19 21 22 23 24 26, so it is 22.
- (23 – 21.7) + (19 – 21.7) + …+(22 – 21.7) = 0
- Attn.! If you do not keep the second digit after the decimal point, you will not get a zero in (b)!

No. 68

- a. 4.84, found by 121/25
- b. Median = 4.0
- c. Summary: On half the days she made at least 4 appointments. The arithmetic mean number of appointments per day is 4.84.

No. 72

- a. The mean: $3.438 found by 51.57/15
- b. The median: $3.44
- c. The book gives the following reply: the mode is $3.49.
- Here is the dot plot (I managed to obtain it with MegaStat this time! But you can also easily do it by hand):

I would say it is very difficult to claim there is a mode in this distribution.

I disagree with the book.

No. 76

- a. 9, found by 12 – 3
- b. 2.72, found by 13.6/5 where mean = 7.6
- c. 3.5071, found by sq.root of 12.3. Attn.! This is a sample. Therefore, the variance of 12.3 is found by dividing the sum 49.2 by 4, not by 5!
- If you double-click on this table, it will open in Excel and let you see the formulas.

No. 78

If you double-click on this table, it will open in Excel and let you see the formulas.

No. 80

- a. The times are a population because all tables for that night are included.
- (We consider that that statistics represents just that Saturday night, and not some night).
- The sum of all waiting times is 1021 minutes, the shortest is 23 minutes, and the longest 67 minutes. Then:
- b. The mean is 40.84, found by 1021/25. The median is 39.
- The range is 44, found by 67 – 23.
- The standard deviation is 14.55, found by the square root of 5291.4/25. (see Excel file)

No. 85 a,b,c

- a. The mean is 9.1, found by 273/30. The median is 9.
- The range is 14, found by 18 – 4. The standard deviation is 3.566, found by the square root of 368.7/29.
- There are 30 items. This means 5 classes, because 25=32 is the first power of 2 greater than 30. The class interval is 14/5=2.8 promoted to 3. the lower class limit of the first class can be 3 (or 4 if you prefer).

No. 88

MegaStat gives the following output:

- The distribution is symmetric about $220,000 with most of the prices less than $47,000 away from the center .
- The distribution is symmetric about 2200 square feet with most of the sizes less than 250 square feet away from the center.

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