Advanced Math Topics

Chapter 3 Review

Please round all answers to the nearest hundredth and make an answer column, just like the test tomorrow!

1) If x1 = 15, x2 = 7, x3 = 29, x4 = 11, x5 = 15, find…

Σ 4x2

2) The prices of six tennis shoes are shown. Find the mean of the data.

$67, $58, $33, $27, $100, $65

3) Find the standard deviation of the shoe prices.

$67, $58, $33, $27, $100, $65

4) Find an interval for the shoe prices using k = 2.

$67, $58, $33, $27, $100, $65

5) At least what % of the data will fall in the interval? Use Chebyshev’s Theorem and k = 2.

$67, $58, $33, $27, $100, $65

6) In reality, what % of the data is in your interval?

$67, $58, $33, $27, $100, $65

7) Your shot put distance was 43 feet. Find your percentile rank.

Distance(ft.) Frequency

50-59 4

40-49 7

30-39 8

20-29 4

Less than 20 2

8) The prices of six lunches are shown. Find the average deviation of the data.

$8, $7, $12, $8, $4, $6

9) You and 5 friends shot 100 free throws. The results are below. Find your z-score.

67, 58, 33, 27, 98(your score), 65

1) If x1 = 15, x2 = 7, x3 = 29, x4 = 11, x5 = 15, find…

Σ 4x2

Solution Process: Square all values, add them up, then multiply by 4.

Answer: 5844

2) The prices of six tennis shoes are shown. Find the mean of the data.

$67, $58, $33, $27, $100, $65

Solution Process: Add the values and divide by 6.

Answer: 58.33

3) Find the standard deviation of the shoe prices.

$67, $58, $33, $27, $100, $65

Solution Process: Square all values, add them up, then multiply that # by 6. From that answer subtract the sum of the numbers

squared(add them first then square the sum). Divide by 6 times 5 and square root the result.

Answer: 26.38

4) Find an interval for the shoe prices using k = 2.

$67, $58, $33, $27, $100, $65

Solution Process: Multiply the standard deviation (26.38) by 2(the k-value) Subtract this value from the mean to find the lower limit.

Add this value to the mean to find the upper limit.

Answer: 5.57 - 111.09

5) At least what % of the data will fall in the interval? Use Chebyshev’s Theorem and k = 2.

$67, $58, $33, $27, $100, $65

Solution Process: Divide 1 by 2 squared. Subtract that result from 1. Move the decimal point to the right twice.

Answer: 75%

6) In reality, what % of the data is in your interval?

$67, $58, $33, $27, $100, $65

Solution Process: Count how many of the 6 numbers are in the interval 5.57-111.09. Divide that number by 6. Move the decimal place two to the right.

Answer: 100%

7) Your shot put distance was 43 feet. Find your percentile rank.

Distance(ft.) Frequency

50-59 4

40-49 7

30-39 8

20-29 4

Less than 20 2

Solution Process: Find the class mark of interval 40-49 which is 44.5. This is higher than your score so do not add anyone other than yourself in that interval. Add the frequency of all scores below yours (8 + 4 + 2) and ½ of thefrequency tied with you (1). Divide this sum by the total frequency (25) and multiply by 100.

Answer: 58th percentile

8) The prices of six lunches are shown. Find the average deviation of the data.

$8, $7, $12, $8, $4, $6

Solution Process: Find the mean(7.5). Find the deviation from the mean foreach number (0.5, 0.5, 4.5, 0.5, 3.5, 1.5) and find the average of those deviations.

Answer: 1.83

9) You and 5 friends shot 100 free throws. The results are below. Find your z-score.

67, 58, 33, 27, 98(your score), 65

Solution Process: Find the mean(58) and standard deviation(25.75). Subtract the mean from your score(98 – 58) and divide the result by the standard deviation.

Answer: 1.55This means you were 1.55 standarddeviations above the mean.

Tiebreaker:

The variance of a group of data is 121. What is the standard deviation?

Answer: 11

HW

• P. 167 #1-11 Compute only the mean for #7. Winners: Odds only.