Math 2 Unit 4 Data Analysis ApplicationsApril 16, 2012
Group Names: ______
MM2D1. Using sample data, students will make informal inferences about populationmeans and standard deviations.
b. Understand and calculate the means and standard deviations of sets of data.
c. Use means and standard deviations to compare data sets.
d. Compare the means and standard deviations of random samples with thecorresponding population parameters, including those population parameters fornormal distributions. Observe that the different sample means vary from one sampleto the next. Observe that the distribution of the sample means has less variability thanthe population distribution.
MM2D1b
Problem 1: The following are the batting averages from the Ola High School baseball team.
.370, .371, .190, .391, .304, .176, .311, .333, .419,. 333, .368, .319
Construct a table and find the following:
a) Mean
b) Mean Absolute Deviation
c)Variance
d)Standard Deviation
Does this data appear to fit the “normal curve”? Justify your answer using the empirical rule either graphically or numerically.
MM2D1 d
Problem 2: A pharmaceutical company manufactures capsules that contain an average of 507 grams of vitamin C. The standard deviation is 3 grams. Using this information and assuming a normal distribution, answer the following questions.
a) Sketch the model of the normal distribution for vitamin C capsulesb) 68% of the capsules should fall between ______and ______.
c) 95% of the capsules should fall between ______and ______.
d) What percent of the capsulescontainsbetween 507 and 510 grams of vitamin C?
e) What percent of the capsules contains between 498 and 507 grams of vitamin C?
f) What percent of the capsules contains between 501 and 510 grams of vitamin C?
g) Give an example of capsule containing less than 5% of the normal amount of vitamin C.
h) What is the interval that should contain at least 88.9% of the data of the vitamin C capsules?
i) What is the interval that should contain at least 63% of the data of the vitamin C capsules?
j) A capsule holding 512 grams would fall between the ______percentile and the ______percentile.
k) A capsule holding 500 grams would fall between the ______percentile and the ______percentile.
MM2D1 c&d
Problem 3: Mr. Turner has two Math 2 classes. With one class, he lectured and the students took notes. In the other class, the students worked in small groups to solve math problems. After the first test, Mr. Turner recorded the student grades to determine if his different styles of teaching might have impacted student learning.
Class 1: 80, 81, 81, 75, 70, 72, 74, 76, 79, 77, 77, 79, 84, 88, 90, 86, 80, 80, 78, 82
Class 2: 70, 90, 72, 89, 86, 86, 86, 86, 84, 82, 77, 79, 84, 84, 84, 86, 87, 88, 88, 88
a) Create two separate line plotsto display the above class data.
b) Compare the shapes of the two distributions and explain how they relate to the empirical rule.
c) What do your answers from a and b lead you to conclude about the measures of spread?
d) What conclusions can be made about how the different teaching styles impacted student learningin Mr. Turner’s classes?