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2.4 Worksheet

The document provides examples of calculating population standard deviation, sample standard deviation, and using standard deviation to estimate the percentage of values that fall within a certain range. It also gives an example of using Chebyshev's theorem to estimate the percentage of values within 2 standard deviations of the mean. Finally, it shows how to approximate the sample standard deviation from a data set involving frequencies and ranges.

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129 views3 pages

2.4 Worksheet

The document provides examples of calculating population standard deviation, sample standard deviation, and using standard deviation to estimate the percentage of values that fall within a certain range. It also gives an example of using Chebyshev's theorem to estimate the percentage of values within 2 standard deviations of the mean. Finally, it shows how to approximate the sample standard deviation from a data set involving frequencies and ranges.

Uploaded by

butterflies spiders
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© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Worksheet 2.

4 Name __________________

A Corporation hired 10 graduates. The starting salaries are as follows:

Salary 40 23 41 50 49 32 41 29 52 58

1. Find the population standard deviation of the starting salaries for the Corporation.

2. Find the sample standard deviation for the Corporation.

3. In a survey conducted by the national Center for Health Statistics, the sample mean height of women in the U.S. (ages
20 – 29) was 64 inches with a sample standard deviation of 2.75 inches. Estimate the percent of the women whose
heights are between 61.25 and 64 inches.

4. Heights of adult women have a mean of 63.6 in. and a standard deviation of 2.5 in. What does Chebyshev’s Theorem
say about the percentage of women with heights between 58.6 in. and 68.6 in?

5. For the following data set, approximate the sample standard deviation.

Miles (per day) Frequency


1–2 9
3–4 22
5–6 28
7–8 15
9 – 10 4
Worksheet 2.4 KEY Name __________________

A Corporation hired 10 graduates. The starting salaries are as follows:

Salary 40 23 41 50 49 32 41 29 52 58

1. Find the population standard deviation of the starting salaries for the Corporation.

40+25+ 41+50+ 49+32+ 41+29+52+58


x́= =41.5
10
1102.5
s2= =110.25
10
s=10.5

2. Find the sample standard deviation for the Corporation.

1102.5
σ 2= =122.5
9
σ =11.07

3. In a survey conducted by the national Center for Health Statistics, the sample mean height of women in the U.S. (ages
20 – 29) was 64 inches with a sample standard deviation of 2.75 inches. Estimate the percent of the women whose
heights are between 61.25 and 64 inches.

The percentage of women between 61.25 and 64 inches is 34%

4. Heights of adult women have a mean of 63.6 in. and a standard deviation of 2.5 in. What does Chebyshev’s Theorem
say about the percentage of women with heights between 58.6 in. and 68.6 in?

1
Chevyshev says P=1− and since 68.6 and 58.6 are 2 standard deviations from the mean then 75% of women have
k2
heights between 58.6 and 68.6 inches.

5. For the following data set, approximate the sample standard deviation.

Miles (per day) Frequency


1–2 9
3–4 22
5–6 28
7–8 15
9 – 10 4

Miles (per day) Frequency xf x−x́ ( x− ´x́ )2 ( x− ´x́ )2 f


1-2 9 13.5 -3.56 12.674 114.06
3-4 22 77 -1.58 0.4336 53.538
5-6 28 154 .44 .1936 5.4208
7-8 15 112.5 2.44 5.9536 89.304
9-10 4 38 4.44 19.714 78.824
∑ ¿78 ∑ ¿395 ∑ ¿341.1808
341.1808
σ=
√ 77
=2.105 mph

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