IB SL Yr 1 Date:

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Name: Unit 7 ReviewOne and Two Variable Statistics Review

7-1 Descriptive Stats. Qualitative (categories) vs. Quantitative( numeric) data. Discrete (countable) vs. Continuous (measurable) data. Bar Graph vs. Histograms Know how to build a frequency table from lists.

7-2 Measures 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.

7-3 Measures of Spread Range– Max- Min Standard Deviation – use σ on graphing calc. but use S for notation. It is the square root of variance.

7-4 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

7-5 Cumulative Frequency A running total of the given data. Know how to interpret a cumulative frequency graph. Know how to draw a graph using a table. Coordinates are ( upper endpoint, Cumulative frequency)

7-6 Representations of cumulative frequency graph. Know how to find a percentile Know how to Calculate an inter quartile range IQR :Q3−Q1 75th percentile – 25th percentile.

7-7 Bivariate Data- Describing relationships and scatterplots Know how to describe a plot: Strength ( Strong, moderate, weak), Direction( positive, Negative) Know how to draw a suitable Line of best fit (through the mean, mean point).

7-8 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.

7-9 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.

Calculator NotesIf you have one list of numbers, fill in L1 if you have two lists of numbers, Linear regression

an x-list and a frequency Fill- in L1, L2

1. Several candy bars were purchased and the following table shows the weight and the cost of each bar.

Yummy Chox Marz Twin Chunx Lite BigC Bite

Weight (g) 60 85 80 65 95 50 100 45

Cost (Euros) 1.10 1.50 1.40 1.20 1.80 1.00 1.70 0.90

(a) Find the correlation coefficient, r, giving your answer correct to 3 decimal places.

(b) Describe the correlation between the weight of a candy bar and its cost.

(c) Find the equation of the regression line for y on x.

(d) Use your equation to estimate the cost of a candy bar weighing 109 g.

2. If the independent and dependent variables show a positive correlation then as the independent variable increases the dependent variable _______________.

If the independent and dependent variables show a negative correlation then as the independent variable increases the dependent variable _______________.

3. This table shows the rainfall in cm in Tennessee from 2000 to 2008.

Year 2000 2001 2002 2003 2004 2005 2006 2007 2008Rainfall 42 51 39 44 31 33 30 28 21

a. Show this data on a scatter diagram.

b. Describe the correlation.

c. In general, what has happened to the rainfall since the year 2000?

4. The table below shows the number of hours spent studying and the increase in the students’ grades in mathematics.

Hours Studying

0 1 2 3 4 5 6 7 8

Increase in Grade

-1 1 3 7 9 9 8 10 14

a. Find the mean point.

b. Construct a scatter diagram and draw a line of best fit through your mean point.

c. Describe the correlation.

d. Determine the equation of the line of best fit.

5. Is there a relationship between grams of fat and the total calories in the data set below?

a. Find the mean number of grams of fat.

b. Find the mean number of calories.

c. Determine the equation of the line of best fit.

d. Predict the total number of calories if the food item has 35 grams of fat. Would this be considered a reliable prediction? Explain.

6.

7. SKIP A!

8. Three positive integers a, b, and c, where a < b < c, are such that their median is 11, their mean is 9 and their range is 10. Find the value of a.

9. The table shows the scores of competitors in a competition.

Score 10 20 30 40 50

Number of competitors with this score 1 2 5 k 3

The mean score is 34. Find the value of k.

10. The following table shows the mathematics marks scored by students.

Mark 1 2 3 4 5 6 7

Frequency 0 4 6 k 8 6 6

The mean mark is 4.6.

(a) Find the value of k.

(b) Write down the mode.

11. At a conference of 100 mathematicians there are 72 men and 28 women. The men have a mean height of 1.79 m and the women have a mean height of 1.62 m. Find the mean height of the 100 mathematicians.

12.

c) There are 60 data values in the set. Estimate the number of values that are less than 10.

13.

14.

15.

16.

A)

17.

a)

B)

b)

18.

19.

A)

B)

A)

B)

20.

C)

A)

B)

C)

21. Consider this set of data: 19, 7, 22, 15, 14, 10, 8, 28, 14, 18, 31, 13, 18, 19, 11, 3, 15, 16, 19, 14

a. Find the 5-number summary below:

Minimum =

First Quartile =

Median =

Third Quartile =

Maximum =

b. Find the range and IQR of the data.

c. Are there any outliers? Show the work that leads to your answer.

d. Draw a box and whisker plot for the data set.

22.23.24.

22. A class of seniors at Quarry Bank School was surveyed to find out how many IB classes they are taking this year. The results are summarized in the table below.

Number of IB courses Frequency0 241 292 k3 494 305 36

23. a. The mean number of IB courses is 2.7. Find the value of k .

b. Find the standard deviation for the number of IB courses taken.

c. Find the median number of IB courses taken.

24. A group of students was surveyed to find out how many books they had read in the past year. The results are summarized in the table below.

Number of books Frequency0 121 62 83 2

4 95 136 k7 15

a. The mean number of books read is 3.92. Find the value of k .