Name: 13-3 Final ReviewPeriod:

13-3 Final review-Units #7-9Directions: The following are Topics that we covered in Units #7-9 Your task is to:

1. Read the Key Ideas/Tips on your own and highlight important ideas/concepts.(everyone does this)

2. Answer the sample IB Question and look up to check answers. (Everyone does this)3. If you find that you get stuck on a question or if you get ANY PART OF THE QUESTION wrong, go to

Google classroom to and watch a teacher take you through the main ideas of the unit and the answer to that question. Then move on to review questions.

4.

Unit Cram Sheet/Big IdeasSample question/s

Working with ONE variableMeasures of center Mean – is the statistical name for its arithmetic average. x=mean : Know

how to read and use Formula booklet formula. DON’T FORGET TO USE L2 in your calc ONLY IF YOU HAVE A QUEQUENCY COLUMN.

Median – is the middle value of an ordered data set. This is also the 50th percentile. To find the location of median (n+1)/2

Mode – is the most frequently occurring value in the data set Know how to use mid-interval value to estimate mean.Measures of Spread Range– Max- MinStandard Deviation – use σ on graphing calc. but use S for notation. It is the square root of variance.

Box Plots 5 Number Summary

o Min,o Lower Quartile (Q1)- is the 25th percentileo Mediano Upper Quartile (Q3) – is the 75th percentileo Max

To test for outliers: low: Q1−1.5( IQR) high: Q3+1.5( IQR)

IQR :Q3−Q1

Representations of cumulative frequency graph. Know how to find a percentile ( look right) Know how to Calculate an inter quartile range IQR :Q3−Q1 75th

percentile – 25th percentile.

Calculator NotesIf you have one list of numbers

1.1. The box and whisker diagram shown below

represents the marks received by 32 students.

(a) Write down the value of the median mark.

(b) Write down the value of the inter quartile range.

(c) Estimate the number of students who received a mark greater than 6.

Working with TWO variables

Bivariate Data- Describing relationships and scatterplots Know how to describe a plot: Strength ( Strong, moderate, weak),

Direction( positive, Negative)Linear Regression/Line of best fit and Correlation coefficient. Know how to use the calculator to write the linear regression of bivariate data. Know how to interpret the correlation coefficient, strength and direction.

Know how to interpret the slope and y intercept of a linear regression equation.

Know how to draw a suitable Line of best fit (through the mean, mean point).

Finding the Correlation CoefficientYou only have to do this ONCE, do it now… Hit 2nd, 0, scroll down to DiagonisticOn. Hit Enter Twice. The screen will say Done. You never have to do this again.- Press Stat: 1: Edit to enter the costs from the table

above into the list editor.- Press the Stat button, then arrow over to Calc.- Choose #4 LinReg(ax+b)- When you press enter, you must tell the calculator which lists

to use for the analysis.- The first list will be X, the second list will be Y.

- To write the regression line,Use the same steps to find the Correlation coefficient, but plug in the slope (a) and Y-intercept (b) to 3 sig figs.

Predictions. Know how to use the line of best fit to make predictions. Interpolation good making a prediction using an X value inside the data

set reliable. ExtrapolationBad making predictions using an x value outside the data

set not reliable.

(a). Use the graph to answer the following.(i)Estimate the interquartile range.

(ii)Given that 40 % of the fish have a length more thank cm, find the value of k.

.

In order to sell the fish, the fisherman classifies them as small, medium or large. Small fish have a length less than 20 cm. Medium fish have a length greater than or equal to 20 cm but less than 60 cm. Large fish have a length greater than or equal to 60 cm.(b)Write down the probability that a fish is small.

The cost of a small fish is $4, a medium fish $10, and a large fish $12.(c)Copy and complete the following table, which gives a

probability distribution for the cost $X.

(d)Find E(X)

Unit Cram Sheet/Big IdeasSample question/s

Probability model has two parts: All poss. Outcomes and their probabilities.

Sum of Probability distribution should be 1.

Know how to create a prob distribution given a formula for probability. Know what a random variable is and understand what it stands for in a

probability situation. The mean or expected value of a random variable X is the average

value that we should expect for X over many trials of the experiment.

Calculate Binomial probabilities of “exact” values using given formula.

2. 1.

Unit 8- Probability

Unit 7 - One variable and two Variable Statistics

You MUST know what each piece of the formula is. What does each number represent?

Calculate binomial probabilities of “at most” situations. You must know what this looks like in ≤ , ≥ symbols.

Calculate binomial probabilities of “at most” situations. You must know what this looks like in ≤ , ≥ symbols.

Know how to identify that it is a binomial distribution. Two outcomes? n?

Know how to calculate the mean(Expected value)/ variance using the formula.

NORMAL DISTRIBUTIONRECALL-standard deviation is the square root of variance.

Z-score is the number of standard deviations away from the mean. The standard Normal curve is the standardized curve- uses Z scores Mean is always 0, standard deviation is always 1.

Know how to sketch the normal curve with appropriate shaded probability.

REMEMBER use -100,000,000 for lowest Value and 100,000,000 for highest value. Normalcdf( Low value, upper value,mean, stad.Dev)

Be able to recognize when to use Z-scores ( mean 0, Standard Dev 1 and when to use x scores ( mean given, standard given).

Understand NOTATION

vs

Recognize when to use INVNORM when solving for VALUE ( x or y or L) or solve for z score –BE CAREFUL HERE, if you want a z score MEAN SHOULD BE 0 and STAN. DEV 1)

REMEMBER: ALWAYS GIVE THE CALC. THE % BELOW, or PERCENTILE.

Use the Z score formula to solve for mean or standard deviation.

3.

1. X~N(μ ,σ) and P(X>58.39) = 0.0217 and P(X<41.82) = 0.0287. Find the value ofμ .∧σ.

At least= 1-binomcdf(n,p, 1less that # in symbol)

At most= binomcdf(n,p,x)

If given two probabilities use shortcut to help you solve for σ first.

σ= ∆ x∆ Z , to find Z scores use INVNORM()

σ= ∆ x∆ Z z= x−μ

σ

Unit Cram Sheet/Big IdeasSample question/s

You should know how to: Use SohCahToa to solve for sides and angles of a right

triangle.

Know how to sketch a diagram and label the angle of elevation/depression correctly.

Sketch a given angle onto the quadrants and find it’s reference angle.

Given an angle find the coterminal angle in standard position.

The exact values of sine, cosine and tangent functions at 0, 30, 45,60 and 90 degrees.

Understand that the values of the coordinates on the unit circle are equivalent to ( cos θ , sin θ)

Know how to convert between radians and degrees using

the conversion dr=180

π.

Know how to simplify trig expressions in different forms.

1. Evaluate:

sin2( π2 )−cos2( π

2 )

Mixed practice

1.

Unit 9- Trig and the Unit CircleUnit 8- Probability Continued

2.

3. The sketches below represent scatter diagrams for the way in which variables x, y and z change over time, t, in a

given chemical experiment. They are labelled 1 , 2 and 3 .

1 2 3tim e tim e tim et t t

x y z

× ×× ×× ×× × × ×××

× ××××

× × ×× × ×

× ×× × ×

× ×× ×

× ×

×

× ×× ×

× ××××

××

××

(a) State which of the diagrams indicate that the pair of variables(i) is not correlated;

(ii) shows strong linear correlation.

(b) A student is given a piece of paper with five numbers written on it. She is told that three of these numbers are the product moment correlation coefficients for the three pairs of variables shown above. The five numbers are

0.9, –0.85, –0.20, 0.04, 1.60(i) For each sketch above state which of these five numbers is the most appropriate value for the

correlation coefficient.

(ii) For the two remaining numbers, state why you reject them for this experiment.

4. Tania wishes to see whether there is any correlation between a person’s age and the number of objects on a tray which could be remembered after looking at them for a certain time. She obtains the following table of results.

Age (x years) 15 21 36 40 44 55Number of objects remembered (y) 17 20 15 16 17 12

(a) Use your graphic display calculator to find the equation of the regression line of y on x. (2marks)

(b) Use your equation to estimate the number of objects remembered by a person aged 28 years. (1marks)

(c) Comment on your faith in this prediction.(1marks)

(d) Use your graphic display calculator to find the correlation coefficient r. (1marks)

(e) Explain what you value for r tells you about the relationship. (2marks)

5.

6.

7.

8.

9.

10. The following frequency distribution has mean 3.8.

a. Calculate the value of k. Show work to justify your answer

b. Find the median number. Show work to justify your answer.

11. The number of club members of each gender choosing each game in a particular year is shown in the table below.

Billiards Snooker DartsMale 39 16 8Female 21 14 17

A club member is to be selected at random. What is the probability that the club member selected

a. is female and likes darts?

b. is a male?

c. likes billiards, given that they are male?

Number (x) 1 2 3 4 5 6Frequency (f ) 5 k 16 18 20 7

12. . The exam results for 100 boys are displayed in the following diagram:

13. 0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 1 0 0

a. Find the range of the results.

b. Find the interquartile range.

c. How many boys scored over a 50 on this exam?

13. In the research department of a university, 300 mice were timed as they each ran through a maze. The results are shown in the cumulative frequency diagram opposite.

(a) How many mice complete the maze in less than 10 seconds?

(b) Estimate the median time.