entering probability and statistics - miss-stow-math - home · · 2017-07-27there are 8 entries...

Entering Probability and Statistics

Summer Assignment

TKCS

Name:____________________________ Instructions:

• Show all work in a neat and organized manner. • You may receive help from any resource you want as long as you understand how to do each

problem • This packet must be completed and turned in the first day of school

Topic: Summation Notation

http://www.mathsisfun.com/algebra/sigma-notation.html

www.miss-stow-math.wikispaces.com (look under Algebra 2)

Example 1: 3𝑘!!!!

Solution: 3 1 + 3 2 + 3 3 + 3 4 + 3 5 =

3+ 6+ 9+ 12+ 15 = 45

Example 2: 𝑘!!!!!

Solution: 1! + 2! + 3! + 4! =

1+ 4+ 9+ 16 = 30

Directions: Evaluate each expression. Show work.

1. (2𝑘 − 7)!!!!!

2. 8𝑘! − 3𝑘!!!!

3. (4𝑘! − 2𝑘 + 8)!"!!!

4. 𝑘!""!!!

Topic: Slope of a Line (given two points)

http://www.coolmath.com/algebra/08-lines/06-finding-slope-line-given-two-points-01


Example 1: Find the slope of the line that passes through (1,2) and (3,4)

Solution: !!!!!!

= !!!!= 1


Solution: 𝟖!𝟔𝟏!𝟑

= !!!= −1

Directions: For the problems below, find the slope of the line between each of the two given points. Show work. Write your answer in simplest form.

5. (1,5) and (7,8)

6. (-5,9) and (5,11)

7. (12,13) and (7,13)

8. (-8,2) and (-8,7)

Topic: Writing equations of lines (using slope and y intercept)

http://www.regentsprep.org/regents/math/algebra/AC1/EqLines.htm


Slope Intercept Form: 𝒚 =𝒎𝒙+ 𝒃

Example 1: Find the slope of the line that passes through (1,2) and has a slope of 5.

Solution: Plug in the slope (m) and point (x,y), then solve for y:

𝑦 − 𝑦! = 𝑚(𝑥 − 𝑥!)

𝑦 − 2 = 5 𝑥 − 1

𝑦 − 2 = 5𝑥 − 5

𝑦 = 5𝑥 − 3


Solution: Plug in the points then solve for y

𝑦 − 𝑦! =𝑦! − 𝑦!𝑥! − 𝑥!

(𝑥 − 𝑥!)

𝑦 − 4 =10− 43− 1 (𝑥 − 1)

𝑦 − 4 =62 𝑥 − 1

𝑦 − 4 = 3𝑥 − 3

𝑦 = 3𝑥 + 1

Directions: Write the equation of the line using the given information. Show work.

9. Passes through (2,4); slope of -3

10. Passes through (-5,8); slope of 1/5

11. Passes through (5,1) and (3,0)

12. Passes through (-2,3) and (-2,-1)

Topic: Permutations

http://www.mathsisfun.com/combinatorics/combinations-permutations.html


Example 1: Evaluate 3P7

Solution: !!!!! !

= !!!!=

7(6)(5)(4)(3)(2)(1)4(3)(2)(1) = 7 6 5 = 210

Example 2: How many different ways can first, second, and third place be awarded to 10

people?

Solution: n=10 people and r=3 (1st, 2nd, 3rd, place)

𝟏𝟎!�𝟎− 𝟑 ! =

10!7! =

10 9 8 7 6 5 4 3 2 17 6 5 4 3 2 1 =

10 9 8 = 720

Directions: Evaluate the following expressions. Show work.

13. 12P3 14. 8P5

15. In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?

16. How many ways can 1st, 2nd, 3rd, and 4th place be awarded to 10 runners?

Topic: Combinations

http://www.mathsisfun.com/combinatorics/combinations-permutations.html


Example 1: Evaluate 3C7

Solution: !!!!! !!!

= !!!!!!

=

7 6 5 4 3 2 14 3 2 1 3 2 1 =

7 6 53 2 1 =

2106 = 35

Example 2: Five cousins at a family reunion decide that three of them will go to pick up a

pizza. How many ways can they choose three people to go?

Solution: n=5 and r=3

𝟓!𝟓− 𝟑 !𝟑! =

5!2! 3! =

5 4 3 2 12(1) 3 2 1 =

5(4)2(1) =

202 = 10

Directions: Evaluate the following expressions. Show work.

17. 12C3 18. 8C5

19. In how many ways can a president, a treasurer and a secretary be chosen from among 7 candidates?

20. From a group of 40 people, a jury of 12 people is selected. In how many different ways can a jury of 12 people be selected?

Topic: Venn Diagrams

http://www.regentsprep.org/regents/math/algebra/AP2/LVenn.htm

Example 1: Out of forty students, 14 are taking English Composition and 29 are taking Chemistry.

If five students are in both classes, how many students are in neither class?

Solution:

Two students are taking neither class

Example 2: Out of forty students, 14 are taking English Composition and 29 are taking Chemistry.

If five students are in both classes, how many students are in either class?

Solution:

There are 38 students in at least one of the classes

Directions: Create a Venn diagram to display the information then solve.

21. In a class of 87 students, 40 take Chorus, 53 take Band, and 16 take both Chorus and Band. How many students in the class are not enrolled in either Chorus or Band?

22. In a school of 800 students, 185 students are taking Spanish, 160 students are on sports teams, and 72 students participate in both activities. How many students don’t participate in either activity?

23. A veterinarian surveys 46 of his patrons. He discovers that 17 have hamsters, 21 have guinea pigs, and 19 have birds. Eight have hamsters and guinea pigs, and 5 people have a guinea pig and a bird. Seven have hamsters and a bird, and of these, 3 people have a guinea pig. How many patrons have none of these pets?

Topic: Stem and Leaf Plots

http://ww.mathsisfun.com/data/stem-leaf-plots.html

www.miss-stow-math.wikispaces.com (Pre Algebra)

Example: Create a Stem and Leaf plot for the following temperatures (in degrees). 63, 63, 70, 72, 74, 82, 86, 95, 101

High Temperature in Oswego (in ℉)

key: 6 3 𝑚𝑒𝑎𝑛𝑠 63℉

Directions: Create a stem and leaf plot, with a key, for each set of data

24. Data: 12, 13, 20, 21, 25, 25, 28, 34, 36, 39, 53, 54, 54, 54, 56, 62, 65, 66, 66, 67, 68, 80, 83, 85, 98

25. Data: 45, 10, 79, 33, 15, 30, 26, 49, 53, 11, 28, 54, 42, 77, 33, 11, 36, 84, 58, 27, 47, 21, 43, 31, 19, 37, 45, 23, 71, 33

Topic: Measures of Central Tendency

http://www.mathsisfun.com/data/central-measures.html


Mean: the average value in a group of

numbers: also called the norm

Add all of the values together to find the total and then divide by the

number of values

4+ 5+ 5+ 6+ 8+ 8= 36

36÷ 6 = 6

6 is the mean

Median: the middle value in a group of

numbers

Place all the values in numerical order and then find the middle

number. If there are two middle values, find the mean of the two middle

numbers

2,4,4,5,6,7,9

5 is the median

Mode: the most frequent value in a group

of numbers

Count how many there are of each value. The number that appears

most often is the mode. You can have more than

one mode!

3, 4, 4, 5, 5, 7, 8, 9

4 and 5 are the modes

Range: the difference between the lowest and

highest values in a group of numbers

Find the lowest and highest values and

subtract the lowest value from the highest value

3, 3, 4, 5, 6, 7, 10, 12

12− 3 = 9

9 is the range

Directions: Find the mean, median, mode, and range for each. Show work.

26. 11, 10, 12, 12, 9, 10, 14, 12, 9

27. 10, 13, 16, 21, 26, 27, 28, 35, 35, 36, 41, 41, 45, 46, 49, 50, 53, 56, 58

Topics: Frequency Tables and Histograms


Example: The following numbers were rolled on a die: 1, 2, 3, 1, 2, 6, 2, 5, 1, 2, 6, 3, 2

Create a frequency table for the data

Solution:

Example: Create a histogram of the frequency table.

Solution:

28. The scores on a mathematics test were 70, 55, 61, 80, 85, 72, 65, 40, 74, 68, and 84. Complete the accompanying table, and use the table to construct a frequency histogram for these scores.

Scores Tally Frequency

40-49

50-59

60-69

70-79

80-89

Topics: Mean, Median, and Mode of Histograms

http://passyworldofmathematics.com/mean-median-mode-for-grouped-data/

Example: Find the mean, median, and mode of the histogram

Solution:

Mean: Find the midpoint of the heights of each bar.

Mean=! !"#.! !! !"#.! !! !"#.! !! !"#.! !! !"#.! !!(!"#.!)!!!!!!!!!!!

= !"#".!!"

= 149.1

Median: Find the middle. There are 25 entries. The 13th entry will be the median. This is at 147.5 (or between 145-150)

Mode: Find the most. There are 8 entries for 152.5 (or between 150-155)

29. Find the mean, median, and mode of the histogram. Show work.

Topics: Quartiles and Box-and-whisker Plots

http://www.regentsprep.org/regents/math/algebra/AD3/boxwhisk.htm

Example: Find the quartiles for the numbers 5, 8, 4, 4, 6, 3, 8

Solution:

1. Put the numbers in order: 3, 4, 4, 5, 6, 8, 8 2. Cut the list into quarters: 3. Identify the quartiles:

a. Quartile 1 (Q1)=4 b. Quartile 2 (Q2), which is also the Median =5 c. Quartile 3 (Q3) = 8

Directions: Find the quartiles (Q1, Q2, Q3) for each

30. 8, 11, 20, 10, 2, 17, 15, 5, 16, 15, 25, 6

31. 13, 18, 6, 20, 25, 11, 9, 18, 3, 30, 16, 9, 8, 23, 26, 17

32. 4, 5, 6, 8, 9, 11, 13, 16, 16, 18, 20, 21, 25, 30, 31, 33, 36, 37, 40, 41

entering probability and statistics - miss-stow-math - home · · 2017-07-27there are 8 entries...

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