Lesson Title

Jackson – Algebra 1 – Statistics -- Notes

Unit Calendar

GRAPHING CALCULATOR USE MANDATORY

Date

Sections

Topic

Homework

HW √

May 11 (B)

May 12 (A)

2 ½ hr block 2

1 hr block 4

13.6

Measures of Central Tendency

Standard Deviation Activity

SOL Prep pack SOLs A2a, 2b, 2c, 9

May 13 (B)

May 14 (A)

2 hr block 1/5

2 ½ hr block 2/6

13.8

Box and Whisker Plots

Calculator Activity

Box and Whisker Plot Practice

SOL Prep Pack SOLs A3, 10

May 15 (B)

May 18 (A)

2 hr block 1

1 hr block 2

1 hr block 4

SOL Review

SOLs A6a, 6b, 7a, 7b, 7c,

SOL Prep Pack SOLs 4a, 4b, 4c, 4d, 4e

May 19 (B) 6, 5, 8, 7

1 hr block 5

May 20 (A) 2, 1, 4, 3

2 hr block 2

1 hr block 1

2 ½ hr block 4

SOL Review

SOL A7d, 7e, 7f , 8

SOL Prep Pack SOLs 5a, 5b, 5c, 5d

May 21 (B)

Algebra 1 SOL

Important: To receive credit for Jefferson Labs SOL questions, email the results to kimberly.jackson@lcps.org. EXTRA credit will be awarded for each set of 5 J-Lab questions completed and emailed.

SOLs: A.9 The student, given a set of data, will interpret variation in real-world contexts and calculate and interpret mean absolute deviation, standard deviation, and z-scores.

A.10 The student will compare and contrast multiple univariate data sets, using box-and-whisker plots.

Vocabulary: mean, median, mode, standard deviation, range, variance, box and whisker plot, lower quartile, upper quartile, interquartile range, outlier.

Textbook resources:Chapter 13.6, 13.8, supplemental material

Statistics

Science of choosing a sample, collecting, organizing, analyzing and interpreting data.

Our working question:

What is the date on which you were born?

(Example: My birthday is September 12, so my response is “12”.)

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Measures of Central Tendency – show the similarities in a set of data

Mean – often referred to as the average.

µ - “mu” is the symbol for mean.∑ is the symbol for the sum.

n represents the number of data elements in the set.

n

What is the mean of our data?

Median – the middle value in a data set when the values are arranged in order, least to greatest

If the number of elements is odd, the median is the middle value.

If the number of elements is even, the median is the average of the two middle values.

What is the median of our data?

Mode – the data element that occurs the most often in the data set.

A data set can have no mode, one mode, or more than one mode.

What is the mode of our data?

Measures of Variation – show the spread or dispersion of the data

Range – the difference between the maximum (largest) and the minimum (smallest) values of the data

What is the range of our data?

Quartiles are values that divide a data set into four equal parts. The median (Q2) separates the data into upper and lower halves. The first quartile (Q1) is the median of the lower half of the data). The third quartile (Q3) is the median of the upper half of the data.

What is the second quartile of our data?

What is Q1 (lower quartile) of our data?

What is Q3 (upper quartile) of our data?

Interquartile Range (IQR) – the difference between Q3 (upper) and Q1 (lower) quartiles.

What is the IQR of our data?

Box-and-Whisker Plot – a graph that summarizes a set of data by displaying it along a number line. It consists of three parts: a box and two whiskers.

(minimummaximummedianQ1Q3)

· The left whisker extends from the minimum to the first quartile. 25% of the data.

· The box extends from the first to the third quartile and has a vertical line at the median. 50% of the data.

· The right whisker extends from the third quartile to the maximum. 25% of the data.

Create a Box-and-Whisker Plot of our data.

1) Find the median.

2) Find the minimum.

3) Find the maximum.

4) Find the first quartile (Q1).

5) Find the third quartile (Q2).

Examples.

Create box and whisker plots for the following data sets:

1) 11, 14, 15, 12, 16, 12, 16, 14, 20

2) 53, 53, 57, 56, 56, 55, 51, 54, 52

Practice.

Create box and whisker plots for the following sets of data:

1) 52, 52, 51, 58, 58, 56, 50, 54, 59

2) 22, 24, 27, 29, 25, 24, 25, 21, 23, 22

3) In a class of 18 students, there are 9 boys and 9 girls. Their quiz scores were as follows:

Girls: 95, 92, 88, 75, 72, 94, 87, 68, 93

Boys: 78, 88, 72, 95, 100, 99, 92, 84, 88

Create box and whisker plots representing both sets of data.

What is the total number of students who scored above an 88 on the quiz?

Central Tendency, part II

The Normal Curve, or Bell Curve, shows the percent of the given data that will fall within a certain distance from the mean of the data. The distances are measured by standard deviations.

~68% of the data will be within 1 standard deviation

~95% will be within 2 standard deviations

The measures of central tendency are:

Variance – the mean (average) of the squared difference

(x represents an element of the data setxi represents the ith element of the data setn represents the number of elements in the data setµ represents the mean of the data set represents the standard deviation of the data set)- Taking the absolute value and squaring the differences addresses the different signs (positive and negative) of the difference.

n

Standard Deviation – the square root of the variance

(n)

Z-score – the number of standard deviations the data value lies above or below the mean.

- positive: the data value is greater than the mean

- negative: the data value is less than the mean

Let’s use our Data to Calculate.

The µ of the class data: ____________________

Xi

Deviation from the Mean

(xi - µ)

Absolute Deviation from the Mean

(|xi - µ|)

Square of the difference from the Mean

(xi - µ)2

X1 =

X2 =

X3 =

X4 =

X5 =

X6 =

X7 =

X8 =

X9 =

X10 =

X11=

X12 =

X13 =

X14 =

X15 =

X16 =

X17 =

X18 =

X19 =

X20 =

X21 =

X22 =

X23 =

X24 =

X25 =

X26 =

Variance =Standard Deviation =

Find YOUR Z-score: ______________

Using the Calculator to find Mean, Standard Deviation, Variance

1) Enter your data into the calculator (STAT, Edit (1)).

2) Press STAT and toggle to CALC and select “1-Var Stats” and press ENTER

3) Your 1-Variable statistics will be displayed.

Example:

Mean – On the formula sheet it is represented as

On the graphing calculator it is represented as

Standard Deviation –On the formula sheet it is represents as

On the graphing calculator it is represented as

Variance – On the formula sheet it is represented as .

It is not on the calculator but you can find it by squaring the standard deviation.

Practice

1) 22, 18, 19, 25, 27, 21, 24

Mean = Standard Deviation =

Variance =

What is the z-score of 22?How many values have a z-score greater than 1?

2) 38, 46, 37, 42, 39, 40, 48, 42

Mean = Standard Deviation =

Variance =

What is the z-score of 40?How many values have a z-score less than 2?

3) The mean speed of vehicles along a stretch of highway is 56 miles per hour with a standard deviation of 4 mph. You measure the speed of three cars traveling along this stretch of highway as 62 mph, 47, mph, and 56 mph. Find the z-score that corresponds to each speed.

4) A certain brand of automobile tire has mean life span of 35,000 miles and a standard deviation of 2,250 miles. The life spans of three randomly selected tires are 34,000 miles, 37,000 miles, and 31,000 miles. Find the z-scores that correspond with each of these tires. Would the life spans of any of the tires be considered unusual?

Practice.

1) 515, 720, 635, 895, 585, 690, 770, 840

Mean = Standard Deviation =

Variance =

What is the z-score of 550?How many values have a z-score less than 1?

2) 116, 105, 117, 124, 107, 112, 112, 125, 110, 113

Mean = Standard Deviation =

Variance =

What is the z-score of 110?How many values have a z-score greater than 2?

3) The average score on the test was 75 and the standard deviation was 8. Antonio was told by the teacher that he had a z-score of -1.5. What was his exam score?

4) A manufacturer of bolts has a quality control policy that requires it to destroy any bolts that are more than 2 standard deviations from the mean. The quality control engineer knows that the bolts coming off of the assembly line have a mean length of 8 cm with a standard deviation of 0.05 cm. For what length will a bolt be destroyed?

Box-and-Whiskers Plots, part II

The box-and-whisker plots below compare the test scores of Ms. Hernandez's and Mr. Johnson’s period one Algebra classes.

 

 

Which is a true statement regarding the data shown?

A:

Ms. Hernandez’s class has a higher mean test score compared to Mr. Johnson’s class.

B:

Ms. Hernandez’s class has a smaller range of test scores than Mr. Johnson’s class.

C:

Ms. Hernandez’s class has a higher median test score than Mr. Johnson’s class.

D:

Ms. Hernandez’s class has a higher upper quartile than Mr. Johnson’s class.

The heights in inches of each member of four basketball teams are represented in box-and-whisker plots.

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Which team has the greatest range in heights?

F: Tigers

G: Spartans

H: Warriors

J: Panthers

There are 21 data items used in creating the box-and-whisker plot below. No numbers in the data list repeat.   

How many of the data items are below 89.5?

A: 5 

B: 10 

C: 15 

D: 16 

Which set of data would create this graph? 

F: 12, 20, 16, 15, 17, 19, 14

G: 12, 13, 15, 16, 16, 18, 20

H: 10, 20, 16, 15, 17, 19, 13

J: 12, 20, 16, 15, 17, 19, 13

Practice.

Here is a list of distances, in miles, that parents in Town A have to drive to take their children to sports practice:

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Here is a list of distances, in miles, that parents in Town B have to drive to take their children to sports practice:

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1) Create a box and whisker plot for each set of data. Put them both on the same number line.

2) Which town has the greater median?

3) Which town has the greater range?

4) Which town has the greater inter-quartile range?

5) Fill in the table below.

Town A

Town B

Mean

Standard Deviation

Variance

6) Which town has a greater standard deviation? What does that mean?

7) What is the z-score of a parent who drives 7 miles in Town A?

8) What is the z-score of a parent who drives 7 miles in Town B?

9) If a parent has a z-score of 1 in Town A, how far do they drive?

10) If a parent has a z-score of 1.5 in Town B, how far do they drive?

11) If a parent has a z-score of 0, what does that tell us about how far they drive?

12) If a parent has a positive z-score, what does that tell us about how far they drive?

13) If a parent has a negative z-score, what does that tell us about how far they drive?

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