Question

4 from unit 1, lesson 9
a student has these scores on ten assignments.
0 40 60 70 75 80 85 95 95 100
the teacher is considering dropping a lowest score. what effect does eliminating the lowest value, 0, from the data set have on the mean and median?

5 from unit 1, lesson 9
a. what is the five - number summary for the data?
2 2 4 4 5 5 6 7 9 15

b. when the maximum, 15, is removed from the data set, what is the five - number summary?

6 from unit 1, lesson 4
the box plot summarizes the test scores for 100 students:
box plot image with test scores from 55 to 100
which term best describes the shape of the distribution?
a bell - shaped
b uniform
c skewed
d symmetric

Explanation:

Problem 4

Step1: Calculate mean with 0

First, find the sum of all scores: \(0 + 40 + 60 + 70 + 75 + 80 + 85 + 95 + 95 + 100 = 600\). There are 10 scores, so the mean is \(\frac{600}{10}=60\).

Step2: Calculate mean without 0

After removing 0, the sum is \(600 - 0 = 600\), and the number of scores is 9. So the new mean is \(\frac{600}{9}\approx66.67\). The mean increases.

Step3: Find median with 0

The data set (sorted) is \(0, 40, 60, 70, 75, 80, 85, 95, 95, 100\). There are 10 values, so the median is the average of the 5th and 6th values: \(\frac{75 + 80}{2}=77.5\).

Step4: Find median without 0

After removing 0, the sorted data is \(40, 60, 70, 75, 80, 85, 95, 95, 100\). There are 9 values, so the median is the 5th value, which is 80. The median increases slightly.

Step1: Identify Minimum

The smallest value in the data set \(2, 2, 4, 4, 5, 5, 6, 7, 9, 15\) is 2.

Step2: Find Q1 (First Quartile)

The data set has 10 values. The first half is \(2, 2, 4, 4, 5\). The median of the first half (Q1) is the 3rd value, which is 4.

Step3: Find Median (Q2)

The median of the entire data set (10 values) is the average of the 5th and 6th values: \(\frac{5 + 5}{2}=5\).

Step4: Find Q3 (Third Quartile)

The second half of the data set is \(5, 6, 7, 9, 15\). The median of the second half (Q3) is the 3rd value, which is 7.

Step5: Identify Maximum

The largest value is 15.

Step1: New Data Set

After removing 15, the data set is \(2, 2, 4, 4, 5, 5, 6, 7, 9\).

Step2: Identify Minimum

The smallest value is 2.

Step3: Find Q1 (First Quartile)

The data set has 9 values. The first half is \(2, 2, 4, 4\). The median of the first half (Q1) is the average of the 2nd and 3rd values: \(\frac{2+4}{2}=3\).

Step4: Find Median (Q2)

The median of the 9 - value data set is the 5th value, which is 5.

Step5: Find Q3 (Third Quartile)

The second half of the data set is \(5, 6, 7, 9\). The median of the second half (Q3) is the average of the 2nd and 3rd values: \(\frac{6 + 7}{2}=6.5\).

Step6: Identify Maximum

The largest value is 9.

Answer:

Eliminating the lowest value (0) increases the mean (from 60 to approximately 66.67) and increases the median (from 77.5 to 80).

Problem 5a