Statistics, Data Analysis, and Probability PS 1.1- Mean, Median, Mode Period 3, 5: 1/3/11 Period: 2, 4, 6: 1/4/11

Mode Mode is the most frequently occurring number in a set. Example: For the set [3, 2, 8, 2, 4] The number that appears most often is 2, so 2 is the mode.

Mode Big Note: If there’s more than one number that appears most often, that’s okay. Some sets will have multiple modes. Example: For the set [3, 2, 8, 2, 4, 3] The numbers that appear most often are both 2 and 3, so the modes of this set are 2 and 3.

continued…Mode For the set [3, 2, 8, 4] Since no numbers appear more than any other numbers, there is no mode for this set.

White Board CFU The box below shows the number of kilowatt-hours of electricity used last month at each of the houses on Harris street. 620, 570, 570, 590, 560, 640, 590, 590, 580 What is the mode of this data?

Mean Mean is often referred to as the “average” of a set of numbers. To find the mean, add up all the values, and divide the sum by the number of values in the set. MEAN= (sum of a group of numbers) (NUMBER of numbers in the group)

Example In calculating mean… If the values are 15, 45, and 33 The sum is =93 The number of numbers in the set is 3 So 93÷3=31

Whiteboard CFU Parisa’s four math test scores were 7, 8, 10, and 6. Hector’s test scores were 6, 7, 9, and 10. Charles’ test scores were 8, 10, 10, and 9. What is Hector’s mean score?

Median Median is the middle number in an ordered set. You must put the numbers in order. In an even set of numbers, the median is the mean of the two middle terms.

Example For the set [3, 7, 8, 2, 4] These numbers aren’t in order, so place them in order: 2, 3, 4, 7, 8 The middle number is 4, so 4 is the median.

Whiteboard CFU Find the median for the following set [3, 7, 8, 2, 4, 6]

ANSWER 4 and 6 are both in the middle The average of 4 and 6= 5, so the median of this set is 5.

PS 1.2- Probability Probability refers to the likelihood that a certain event will happen, such as flipping heads or tails on a coin, or pulling particular color of marble out of a bag.

Probability The probability of an event occurring is always the number of DESIRED outcomes The TOTAL POSSIBLE outcomes

Example For instance, if you’ve got a deck of cards and you want to pull out a spade, the number of desired outcomes (what you want to happen) would be 13, since there are 13 spades in a deck of cards. The number of total possible outcomes would be 52, since there are 52 total cards in the deck. Therefore: the number of DESIRED outcomes= 13 = 1 the TOTAL POSSIBLE outcomes 52 4 So the probability of picking a spade would be 1/4 or 25%.

BIG NOTE The CAHSEE will try to trick you on probability problems. If the previous example has told us that the ace of spades had been removed from the deck, and then we were to choose a card, that would change how we determine the probability.

Big Note continued… Since one of the spades had been removed, there would only be 12 spades (instead of 13), so 12 would have been the number of desired outcomes. Also, removing that one card from the deck means that there would only be 51 total cards.

BIG NOTE #2 Another common trick involves understanding what doesn’t affect probability. Let’s say you flipped a coin ten times, and it came up heads every single time. What would be the probability that it came up heads on the eleventh flip? * Getting heads ten times in a row may be unlikely, but it doesn’t affect probability on the eleventh flip.

WHITE BOARD CFU A bucket contains 3 bottles of apple juice, 2 bottles of orange juice, 6 bottles of tomato juice, and 8 bottles of water. If Kira randomly selects a bottle, what is the probability that she will select a drink other than water?

ANSWER DESIRED outcomes= 11 TOTAL POSSIBLE outcomes= 19 = 11 19

Independent Practice Independent Practice PS 1.2 1) Drawing a 6 from a deck of cards? 2) Drawing a black card from a deck of cards? 3) Rolling an odd number on a die? 4) Drawing a 3 from a deck of cards? 5) Drawing a club from a deck of cards? 6) Rolling an even number on a die? 7) Rolling a 6 on a die? Independent Practice PS 1.1 1) 18, 18, 15, 18, 18, 24, 21, 21, 24, 14 2) 94, 69, 84, 69, 90, 75, 94, 90, 90, 9, 5 3) 4, 18, 18, 23, 23, 19, 8, 8, 8, 8, 28 4) 12, 15, 16, 17, 15, 17, 17, 17, 18, 17 5) 16, 3, 3, 3, 8, 24, 16, 9, 11, 11 6) 22, 5, 22, 13, 12, 24, 24, 9, 24, 19 7) 23, 1, 1, 18, 1, 3, 18, 10, 7, 3 8) 23, 10, 2, 6, 10, 14, 1, 19, 8, 19