# Essay on Statistics

Data File 2 - Chapter Three (Show all your work) 1) A teacher asked each of her students how many novels they had read in the previous six months. The results are shown below.

0 1 5 4 2 1 3 2

2 7 2 5 0 1 0 1

1 2 6 0 2 3 1 2

7 1 4 2 3 1 7 0

0 2 1 1 0 6 1 7

Construct a frequency table for the number of novels read.

Solution:

Number of novels read | Frequency | 0 | 7 | 1 | 11 | 2 | 9 | 3 | 3 | 4 | 2 | 5 | 2 | 6 | 2 | 7 | 4 |

2) The frequency table shows the weights in ounces of 30 stones

Weight (oz) Number of Stones

1.2-1.6 5

1.7-2.1 2

2.2-2.6 5

2.7-3.1 5 3.2-3.6.1.1 13

Use the above information to construct a cumulative frequency

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Solution: The mode is 43 because this value occurs most often in the sample data. 4) The mathematics SAT scores of the seven students in a mathematics seminar are 533, 553, 578, 586, 619, 626, and 633. Suppose that the student with the score of 533 drops the seminar and is replaced by a student with a score of 765. What will happen to the mean and the median scores of the class? Explain.

Solution: 4128 | sum | | 589.7143 | | Mean | 589.7 | | Median | 586 | | | | | | | | | | | 4360 | sum | | 622.8571 | | Mean | 622.9 | | Median | 619 |

They both increase. Since the mean is the average score, dropping the lowest score and adding a higher score will increase the average. The median is the middle score, so dropping the lowest score and adding a new highest score has the effect of moving the middle score up to the next student.

5) Suppose there are 400 students in your school class. What class rank is the 20th percentile?

Solution: The 20th percentile is the value that separates the bottom 20% of the 400 students from the top 80%. In other words, the 20th percentile is greater than or equal to at least