Algebra 1 A.9 A.10 Statistics Study Guide Page 1

Name: ___________________________________________ Date: _______________ Block: __________

SOL A.9, A.10 Statistics Test Study Guide Know how to:

Find the mean, median, mode, and range for a set of data, and compare these measures.

Identify the parts of a box-and-whisker plot, and compare data in these plots.

Find the Mean Absolute Deviation (MAD), standard deviation (σ), and variance (σ2) for a set of data.

Find the z-score for a data point in a set of data.

Given a z-score, mean, and standard deviation, find the data point with that z-score.

Interpret data based on z-score.

Use the formulas to calculate MAD, σ, σ2, and z-score related information. SOL FORMULA SHEETS MAY BE USED ON THE TEST!

o Deviation is how far a data point is above or below the mean (x – μ). Can be positive or negative,

o MAD is the mean of the distances (absolute value) of each deviation.

o Variance (σ2) is the mean of the squares of the deviations.

o Standard Deviation (σ) is the square root of variance.

o Z-score is how many standard deviations a data point is above or below the mean. Can be positive or negative.

Sample questions (round to the nearest hundredth as necessary):

1) Judy likes to track her savings account. The box and whisker plot shows how much money she

had daily over the past two months. a) What is the range of the amount of money in Judy’s account?

b) What is the inter-quartile range of the amount of money in Judy’s account?

c) What fraction of the time was the account between $51and $68?

d) What percent of the time is the account between 18 and 87?

e) What is the value of the lower quartile?

f) What is the value of the lower extreme?

g) What is the value of the median?

h) What fraction of the time did the account have $51 or less?

i) Which quarter has the data the most spread out?

j) Which quarter has the data the most clustered?

k) What percent of the data falls between the upper quartile and the upper extreme?

l) What percent of the data is greater than the lower quartile?

Algebra 1 A.9 A.10 Statistics Study Guide Page 2

2) Part 1: The chart at right shows the scores for each of Sam and Mary’s

math grades for a school term. Using this chart, create a stacked box and whisker plot to compare Sam’s and Mary’s math grades.

Part 2:

Using the data from the same chart at right, which of the following is

true?

a) The range for Sam’s data is less than Mary’s range.

b) The mean for Mary’s data is the same as the median for Sam’s data.

c) Mary’s mean score is less than Sam’s mean score.

d) Mary’s median score is higher than her mean score. 3)

The stacked box and whisker plots above track the stock performance of four leading companies.

a) Which company holds the record for the most stocks sold? How many did they sell?

b) Which company has the greatest median amount of stocks sold?

4)

The box-and-whisker plot above compares homework time and tv time for a class of 8th grade Algebra students. Which statement is false?

a) The upper quartile for homework time is the same as the median for tv time.

b) The interquartile range for tv time is less than that for homework time.

c) The range for tv time is greater than the range for homework time.

d) The MAD for homework time is most likely less than the MAD for tv time;

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5) Find the mean, mean absolute deviation (MAD), variance (σ2), and standard deviation (σ) for

the data sets below:

a) {12, 18, 35, 10, 50} b) {96, 82, 100, 90, 71, 83} c) {450, 600, 411, 382, 550, 520, 475}

6) Suppose the data from question 5c above represents the Algebra SOL scores for some

students.

a) Find the z-score of each score

b) How many of these SOL scores fall within one standard deviation of the mean?

c) How many standard deviations are required to contain all of the data?

7) Alice and Martin are in the same French class. The following represent class scores for this test:

{100, 82, 97, 75, 85, 82, 85, 90, 93, 70, 66, 80}

a) Find the mean and standard deviation for the data.

b) Alice’s test score was a 97. How many standard deviations is her score from the mean?

c) Martin’s scored 0.89 standard deviations below the mean. What was his test score (to the nearest whole number)?

8) Barbara took two tests:

On her English test, she received a score of 38. The mean of the class was a 35 and the standard deviation was 0.5. On her physics test, she received a score of 52. The mean of

the class was 49 and the standard deviation was 0.8.

On which test did she do better? Explain your answer.

9) The mean height for US males is 70 inches with a standard deviation of 2.8. The mean length of a cat is 18 inches with a standard deviation of 1.2. Mr. Jones is 66 inches tall, and his cat Mr. Tinkles is 16 inches long. Who is shorter, compared to average height for

their respective species? Explain your answer.

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10) The data set shown has a mean of 65.4 and a standard deviation of 26.7, rounded to the

nearest tenth.

{32, 36, 41, 43, 47, 52, 62, 75, 87, 98, 102, 110}

How many of these data points have a z-score greater than -0.4?

11) A data set has a mean of 52.34 and a standard deviation of 6.35. An element in this data set is 41. What is the z-score for 41? Round to the nearest hundredth.

12) A data set has a mean of 24.7 and a standard deviation of 8.93. An element in this data set

is 1.3 standard deviations above the mean. What is the value of the element?

13) The table shows the scores of an Algebra test for four different classes. It also shows the z-

score of one student in the class.

Which student had the highest score on the test?

Mean for the class

Standard Deviation for the class

Student’s z-score

Bob 82 10 1.3

Morris 88 9 1.1

Kathy 84 11 1.4

Robin 79 6 1.8

14) From 1984 to 1995, the winning scores for a golf tournament were: 276, 279, 277, 278, 278, 280, 282, 279, 285, 272, 279, and 278

a) Find the mean and standard deviation for the data (round to the nearest hundredth).

b) Find the z-score of the first 4 unique scores in the list (276, 279, 277, 278)

c) How many of these winning scores fall within one standard deviation of the mean?

Algebra 1 A.9 A.10 Statistics Study Guide Page 5

15) A math class took a test, the results yielded a mean of 89 with a standard deviation of 4. If

students have a z-score less than -2, they have to do a re-take. Use the table below to determine the z-scores for each student and which of these students have to do a retake.

Name Statistics Test Score Z-Score Retake Yes/No

Louis 77

Harry 83

Niall 84

Liam 80

Zayn 81

Justin 91

Algebra 1 A.9 A.10 Statistics Study Guide Page 6

Statistics Test Study Guide Answers

1) a) 82 b) 35 c) 1

4 d) 75% e) 51 f) 18 g) 68 h)

1

4 i) first j)fourth k) 25% l) 75%

2) Part 1: Part 2: b

3) a) company D; about 4150 b) company C

4) b

5a) μ = 25, MAD = 14, σ2 = 233.6, σ = 15.28

5b) μ = 87, MAD = 8.33, σ2 = 92.67, σ = 9.63

5c) μ = 484, MAD = 62.29, σ2 = 5154, σ = 71.79

6a) z-scores: -0.47, 1.62, -1.02, -1.42, 0.92, 0.50, -0.13

6b) 4 scores (450, 550, 520, 575)

6c) 2 standard deviations are needed to contain all data

7a) μ =83.75, σ = 9.87

7b) 1.34 standard deviations above the mean

7c) Martin received a 75 on the test.

8) Barbara’s z-score for her English test is 6, and her z-score for her physics test is 3.75.

She did better on her English test, because she was 6 standard deviations above the mean, while she was only 3.75 standard deviations above the mean for the physics test.

9) Mr. Tinkles is comparatively shorter than Mr. Jones because Mr. Tinkles’ z-score is -

1.67 while Mr. Jones’ z-score is approximately -1.43. So Mr. Tinkles is more short (1.67 standard deviations under the mean) than Mr. Jones (1.43 standard deviations under the mean) compared to their species.

10) 6 points (all the points greater than 54.7)

11) -1.79

12) 36.309

13) Kathy (got a 99.4)

14) a) µ=278.58; σ=3.01 b) -0.86, 0.14, -0.52, -0.19 c) 9 points (between

approximately 275 and 281)

15)

Louis and Liam have to re-retake the test.

Name Statistics Test Score Z-Score Retake Yes/No

Louis 77 -3 Yes

Harry 83 -1.5 No

Niall 84 -1.25 No

Liam 80 -2.25 Yes

Zayn 81 -2 No

Justin 91 .5 No