STATISTICS AND PROBABILITY CHAPTER 4 STAT. & PROBABILITY 4.1 Sampling, Line, Bar and Circle Graphs 4.2 The Mean, Median and Mode 4.3 Counting Problems and Probability 4.1 Unbiased Samples Unbiased sample is a random sample so that each member has an equal opportunity of being selected. 4.1 Example 1. A college president wants to find out which courses are popular with students. What procedure
would be most appropriate for obtaining an unbiased sample of students? A. Survey a random sample of students from the English Department. B. Survey the first hundred students from an alphabetical listing. C. Survey random sample of students from list of entire student body. D. Survey random sample of students from list of entire student body. 4.1 Line and Bar Graphs 2. The graph shows the yearly average temperature from 1980 to 1985. What is the difference between the highest and lowest?
77 76 F 75 74 73 77 - 73 = 4 A. 73 F B. 77 F C. 1 F D. 4 F 4.1 Circle Graphs 4. The number of people employed in different work areas in a manufacturing plant are represented 3
by the circle graph. What percent are represented in Sales and 5 Administration combined? 6 A S 3 8 p = , 40 p =800, p =20 40 100 A. 25% B. 20% C. 2.5% 23
Total = 40 D. 7.5% 4.1 Relations from Data 7. Consider the following graph showing the value of a $15,000 car after 1, 2, 3, 4, 5 and 6 years. In what year did the price of the car begin to stabilize? A. 6 B. 5 C. 4
Trade-in Value for A $15000 Car 10 8 6 4 2 0 1 2 3 4 5 6
Year D. 3 4.1 Predictions from Data Strong Positive Strong Negative Weak Positive None Weak Negative Never select a choice that says one caused the other, as the above graphs do not contain sufficient information to determine cause and effect.
4.1 Predictions from Data 9. The graph shows number of TV 20 adds shown & number of cars sold during a 14 wk. period. Which Cars best describes the relationship sold between the number of ads and cars sold? Ads 14 A. No Apparent association B. Increase in ads caused increase in sales C. Increase in sales caused increase in ads
D. There is a positive association between increase in ads and increase in sales 4.2 Mean, Median & Mode Mean - sum of elements in set divided by number of elements in set. Median - middle element when arranged in order or average of two middle elements. Mode - most frequent element(s). If no element occurs more than once then there is no mode. 4.2 Mean, Median & Mode 1. Find mean, median & mode of the data in this sample: 6, 15, 24, 23, 29, 22, 21, 29, 29 A. 22, 23,29 Arrange in order:
6, 15, 21, 22, 23, 24, 29, 29, 29 Mode is 29 (most frequent) B.17.5, 22,29 Median is 23 (middle) C. 29, 23,22 Average too large! (6+15+21+22+23+24+29+29+29)/9 D. 23, 22,29 198/9=22 the mean 4.2 Relationships & Graphs NORMAL SKEWED Left 0 Mean = Median = Mode 100
Mean < Med. < Mode SKEWED Right 0 100 Mode < Med.< Mean 4.2 Example 3. In a literature class, half scored 95 on a test. Most of the remaining scored 65, except for a few who scored 20. Which is true?
Test Scores for 40 Students 20 15 10 5 0 20 A. The mode equals the mean. 95 Mean < Med. < Mode B. The median is greater than mode C. The mode is greater than mean D. The mean is greater than mode 65
Scores Half scored 95 means mode =95 4.2 Applications 8. The table shows the percent distribution of households by income level in 1990. What percent of the families have income of at least $35,000? Income Level 0 - $4999 $5000 - $9999
$10,000 - $14,999 $15,000 - $24,999 $25,000 - $34,999 $35,000 - $49,000 $50,000 - $74,999 $75,000 and over % of Families 6 11 10 19 16 17 13 7 17+13+7=37
A. 47 B. 53 C. 26 D. 37 4.3 The Counting Principle To count the number of ways a sequence of events can happen, multiply the amount of ways each can occur. 1. Students are asked to rank 4 instructors from best to worst. How many different ways can the 4 instructors be ranked? 4 3 2 1
_______ x ________ x __________ x ________ 1st A. 1 2nd B. 4 3rd C. 64 D. 24 4th
4.3 Computing Probability It must always be the case: 0P(E)1 P(not E) = 1- P(E) P(A or B) = P(A) +P(B) - P(A and B) A and B are called mutually exclusive when P(A and B)=0 and then P(A or B) = P(A) +P(B) 4.3 Computing Probability To calculate P(A and B) P(A and B)= P(A)P(B|A) P(B|A) is the probability of B given A has occurred. A and B are called independent events if and only if P(B| A)=P(B) and then P(A and B) = P(A)P(B) Two events are dependent if and only if the occurrence
of one event affects the probability of the other. 4.3 Example A survey at a college indicated that 90% of those taking the Essay portion of CLAST passed. If only 70% of those taking Math passed, what is the probability that a randomly selected student will fail both the Essay and the Math portion? Since 70% passed math, 30% or 3/10 failed and Since 90% passed essay, 10% or 1/10 failed And we will assume the two events are independent 4.3 Example
A survey at a college indicated that 90% of those taking the Essay portion of CLAST passed. If only 70% of those taking Math passed, what is the probability that a randomly selected student will fail both the Essay and the Math portion? P(failed Math)=3/10 and P(failed Essay)=1/10 P(failed Math and failed Essay)=(3/10)(1/10) =3/100 4.3 Example Two common sources of protein for US adults are
beans & meat. If 75% of US adults eat meat, 80% eat beans and 70% eat both meat & beans, what is the probability that a randomly selected adult eats meat or beans? P(meat or beans) =P(meat) or P(beans) =75% + 80% 85% P(both) 70% = 85 17 = = 100 20 4.3 Probability Application
8. The table gives the percent of students at a university by sex and student classification. Find the probability that a randomly selected student is a senior. Male Female Fresh. 16% 14% Soph. 13% 15% Junior 10% 12%
Senior 11% 9% 20 20% = =0.20 11% + 9% = 20%, 100 A. 0.20 D. 0.49 B. 0.30 C. 0.52 REMEMBER MATH IS FUN AND YOU CAN DO IT
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