3a-Practice with distributions

3a-Practice with distributions - Practice with...

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Unformatted text preview: Practice with distributions of data Work the following problems. Answers are given at the end. 1. The following data are the number of visits each member of a team of 12 basketball players made to the BK restaurant last week. For instance, player “C” made 2 visits to BK. Find the distribution of the number of visits. Express your answer in terms of percents. person BK visits A 0 B 3 C 2 D 1 E 1 F 0 G 0 H 1 I 2 J 1 K 1 L 4 2. The following data are the weights of 20 college‐age males. Group the data into the following intervals 140‐149, 150‐159, 160‐169, 170‐179, 180‐189. Get the frequencies for each of these intervals and sketch the histogram. 140 141 155 169 153 179 150 176 178 157 160 153 155 184 145 160 163 145 150 185 3. The average verbal SAT score one year was 504. George scored 615, and his mother began bragging that her son did exceptionally well on this exam because his score was 111 points above average. What are we to make of this? a. Mom’s right. George’s score was exceptional. b. We can’t tell without knowing the distribution of scores. (continued next page) 4. As a way to get acquainted, each person in a classroom of 40 students was asked how many siblings (brothers and sisters) he or she has. A frequency distribution is shown below. Sibling Frequencies 14 12 10 8 6 4 2 0 0 1 2 3 4 5 a. What percentage of the people in the classroom have exactly 2 brothers and sisters? b. What percentage of the people in the classroom have 2 or more brothers and sisters? c. What percentage of the people in the classroom have 2 or fewer brothers and sisters? (answers next page) Answers 1. The distribution in table form is shown below. To obtain it, count the number of team members out of 12 who had 0 visits to BK, 1 visit to BK, etc. For instance 3 team members had no visits to BK, 5 had one visit to BK, etc. Then convert to percents. For instance, 3/12 = 25% of the team didn’t visit BK at all last week, 5/12 = 41.7% visited BK once, etc. Number of visits 0 1 2 3 4 total Frequency 3 5 2 1 1 12 Pct. (out of 12) 25% 41.7% 16.7% 8.3% 8.3% 100% 2. The table below shows the frequencies with which individual weights fell in each of the intervals. These frequencies are plotted in a bar graph. The proper display of the histogram does not have spaces between the bars. Typically there are from 5 to 10 intervals for a histogram. The choice of intervals is arbitrary. WT 140‐149 150‐159 160‐169 170‐179 180‐189 Total frequency 4 7 4 3 2 20 (continued next page) 3. The answer is b. How well George did relative to others depends on the distribution of SAT scores. If most of the data were within a few points of the average of 504, then George would have done very well. If the data were spread out, then George may not be as outstanding as Mom thinks. It turns out that George fell in the upper 16% of SAT scores. This is good but not outstanding. 4a. From the heights of the bars, we see that 8 people in the classroom have two brothers and sisters. This is 100×(8/40)% = 20%. 4b. From the heights of the bars, we see that 8 people have two brothers and sisters, 5 people have three brothers and sisters, 3 people have four brothers and sisters, and 1 person has five brothers and sisters. Thus 8 + 5 + 3 + 1 = 17 people have two or more brothers and sisters. This is 100×(17/40)% = 42.5%. 4c. From the heights of the bars 10 people have no brothers and sisters, 13 people have one brother or sister, and 8 people have two brothers and sisters. Thus 10 + 13 + 8 = 31 people have 2 or fewer brothers and sisters. This is 77.5%. ...
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  • Fall '08
  • Boyer
  • Statistics, Harshad number, brothers, 154, person  BK visits

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