Unit 6/7: Data & Statistics

2017

pebblebrook high schoolALGBRA 2

6.1-6.5

6.1 Compound Interest

The Number of times compounded per year can change. Compounded annually, n = 1 Compounded quarterly, n = 4 Compounded semiannually, n = 2 Compounded monthly, n = 12

Section 6.1 Homework

6.2 Mean, Median, & Mode

Example #1: Calculate the mean, median, mode.a) Number of siblings: 0, 1, 2, 3, 4, 5 or more

b) Number of hours you study math: 0, 1, 2, 3 or more

c) 1st digit of cell phone # (NOT THE AREA CODE) 1, 2, 3, 4, 5, 6, 7, 8, 9

A Box and Whisker plots shows the median, the quartiles, and the extremes for a numerical set of data.

The box portion contains about 50% of the data values. The two whiskers each contain about 25% of the data values. It shows how spread out the data values are. They are useful for comparing sets of data.

Least Value: _________________

1st Quartile: __________________

Median: _____________________3rd Quartile: __________________

Greatest Value: _______________Interquartile Range (IQR): _____________

Range: ______________________

Example #2: Create a Box & Whisker Plot

a)Number of siblings: 0, 1, 2, 3, 4, 5 or more

b) Number of hours you study math: 0, 1, 2, 3 or more

c) 1st digit of cell phone # (NOT THE AREA CODE) 1, 2, 3, 4, 5, 6, 7, 8, 9

You Try…..

Using the data:

a) Find the mean, median, & mode

b) Create a Box & Whisker Plot. State the IQR & Range.

Section 6.2 Homework

A. For the following groups of numbers, calculate the mean, median and mode for each.B. Create a Box & Whisker Plot. State the IQR & Range.

1. 18, 24, 17, 21, 24, 16, 29, 18 Mean_______ IQR _______Median______ Range _______

Mode_______

2. 75, 87, 49, 68, 75, 84, 98 Mean_______ IQR _______Median______ Range ______

Mode_______

3. 55, 47, 38, 66, 56, 64, 44, 63, 39 Mean_______ IQR ________

Median______ Range _______

Mode_______

6.3 Standard Deviation & Variance

Variance – a numerical value that tells us how spread out the data is. I.e. range & IQR

Standard deviation – a variance that shows how close to the mean that data are.

Example #1. Calculate the mean & standard deviation.

a)The height (in inches) of 5 preschoolers, age 3.31, 36, 34, 32.5, 34, 33

Data (x) x - xData - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean)2

b) The test scores of 5 students: 95, 78, 83, 63, 62

Data (x) x - xData - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean )2

c) The age of 5 students in Algebra 2: 16, 17, 18, 17, 16

Data (x) x - xData - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean )2

You Try….Use the data to find the mean & standard deviation.

Data (x) x - xData - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean )2

Section 6.3 Homework

#4 #5Data (x) x - x

Data - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean)2

6.4 Normal Distribution

Data (x) x - xData - mean

(x - x)2

(data – mean)2

Average of (data – mean)2

√(data –mean)2

Normal distribution is a visual representation of how the standard deviation and how it compares to the mean.

Skew Left – when majority of the data is above the mean.

Skewed Right – when majority of the data is below the mean.

Normal Curve – is when the mean is in the center of the data.

Example #1: Sketch a normal curve.

a) Mean = 45; Standard Deviation = 5

b) Mean = 80; Standard Deviation = 15

c) Mean = 80; Standard Deviation = 4

Example #2: A set of data has a mean of 62 and a standard deviation of 5.7.

a) Complete the normal distribution curve.

b) What percentage of data falls between 42 and 58?

c) What percentage of data is greater than 34?

d) What percentage of data is less than 50?

Example #3: 174 students took the Algebra 2 final exam. The mean was 68.5 and the standard deviation was 7.3.

a) Complete the normal distribution curve.

b) Find the number of students who received a grade 2 standard deviations above the mean.

c) Find the number of students who received a grade of 61 or below.

d) How many students scored within 1 standard deviation?

Section 6.4 HomeworkQuestion #1

Question #2

Section 6.5 Z-ScoresZ-score – tells the number of standard deviations the value is from the mean.

z-score = value−meanstandard deviation

Example #1: Calculate the z-scoreLewis earned 80 on his biology midterm and a 71 on his history midterm. In the biology class the mean score was 75 with a standard deviation of 4. In the history class the mean score was 73 with a standard deviation of 3.

a. Convert each score to a standard z-score.

b. On which test did he do better compared to the rest of the class?

Example #2: CompareThe scores on a university examination are normally distributed with a mean of 62 and a standard deviation of 11. If the middle 68% of students will get a “C”, what is the lowest mark that a student can have and still be awarded a C?

Section 5.5 Homework1. A normal distribution of scores has a standard deviation of 10. Find the z-score that is 24 points above the mean.

2. A normal distribution of scores has a standard deviation of 5.6. Find the z-scores corresponding to each of the following values:

a) A score of 60, where the mean score of the sample data values is 40.

b) A score of 20, where the mean score of the sample data values is 50.

3. IQ scores have a mean of 100 and a standard deviation of 16. Albert Einstein reportedly had an IQ of 160.

a) Convert Einstein’s IQ score to a z-score.

b) Is Einstein’s IQ usual or unusual? Explain.

4. Women’s heights have a mean of 63.6 in. and a standard deviation of 2.5 inches. Find the z-score corresponding to a woman with a height of 70 inches and determine whether the height is unusual.

5. Three students take equivalent stress tests. Which is the highest relative score: A, B, or C? SHOW ALL WORK!!

a) A score of 144 on a test with a mean of 128 and a standard deviation of 34.

b) A score of 90 on a test with a mean of 86 and a standard deviation of 18.

c) A score of 18 on a test with a mean of 15 and a standard deviation of 5.