Mathematics: Find the standard deviation of the following set of data

Find the standard deviation of the following, №10781049, 13.10.2020 08:43

Mathematics

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures.

Step-by-step answer

P Answered by PhD

Explained below.

Step-by-step explanation:

The question is:

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}

Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}

The five-number summary is:

MinimumFirst Quartile Median Third Quartile Maximum

The five-number summary for set A is:

Variable Minimum Q₁ Median Q₃ Maximum

Set A 36.00 38.25 44.00 50.75 54.00

The five-number summary for set B is:

Variable Minimum Q₁ Median Q₃ Maximum

Set B 22.00 28.75 48.00 58.50 65.00

Compute the mean for both the data as follows:

$Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6$

Both the distribution has the same mean.

Compare mean and median for the two data:

$Mean_{A}Median_{A}\\\\Mean_{B}Median_{B}$

This implies that set A is positively skewed whereas set B is negatively skewed.

Compute the standard deviation for both the set as follows:

$SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6$

The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.

Mathematics

What is the standard deviation of company r s earnings per month for this year? (1) the standard deviation of company r s earnings per month in the first half of this year was $2.3 million. (2) the standard deviation of company r s earnings per month in the second half of this year was $3.9 million. 2. what is the standard deviation of q, a set of consecutive integers? (1) q has 21 members. (2) the median value of set q is 20. 3. lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. if

Step-by-step answer

P Answered by Master

9

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 are all factors of 2

Mathematics

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. Set A Set B The distributions are symmetric, so use the means and standard deviations. The mean for Set A is about 44.6 with standard deviation of about 6.2. The mean for Set B is about 42.8 with standard deviation of about 1.86. While the average low temperatures for the cities are approximately equal, the greater standard deviation for Set B means that Set A’s low temperatures have a greater variability than Set B temperatures.

Step-by-step answer

P Answered by PhD

Explained below.

Step-by-step explanation:

The question is:

Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

Set A: {36, 51, 37, 42, 54, 39, 53, 42, 46, 38, 50, 47}

Set B: {22, 57, 46, 24, 31, 41, 64, 50, 28, 59, 65, 38}

The five-number summary is:

MinimumFirst Quartile Median Third Quartile Maximum

The five-number summary for set A is:

Variable Minimum Q₁ Median Q₃ Maximum

Set A 36.00 38.25 44.00 50.75 54.00

The five-number summary for set B is:

Variable Minimum Q₁ Median Q₃ Maximum

Set B 22.00 28.75 48.00 58.50 65.00

Compute the mean for both the data as follows:

$Mean_{A}=\frac{1}{12}\times [36+51+37+...+47]=44.58\approx 44.6\\\\Mean_{B}=\frac{1}{12}\times [22+57+46+...+38]=44.58\approx 44.6$

Both the distribution has the same mean.

Compare mean and median for the two data:

$Mean_{A}Median_{A}\\\\Mean_{B}Median_{B}$

This implies that set A is positively skewed whereas set B is negatively skewed.

Compute the standard deviation for both the set as follows:

$SD_{A}=\sqrt{\frac{1}{12-1}\times [(36-44.6)^{2}+...+(47-44.6)^{2}]}=6.44\approx 6.4\\\\SD_{B}=\sqrt{\frac{1}{12-1}\times [(22-44.6)^{2}+...+(38-44.6)^{2}]}=15.56\approx 15.6$

The set B has a greater standard deviation that set A. Implying set B has a greater variability that set B.

Mathematics

What is the standard deviation of company r s earnings per month for this year? (1) the standard deviation of company r s earnings per month in the first half of this year was $2.3 million. (2) the standard deviation of company r s earnings per month in the second half of this year was $3.9 million. 2. what is the standard deviation of q, a set of consecutive integers? (1) q has 21 members. (2) the median value of set q is 20. 3. lifetime of all the batteries produced by certain companies have a distribution which is symmetric about mean m. if

Step-by-step answer

P Answered by Master

9

2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 are all factors of 2

Mathematics

Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places. 10) Country Number of Television Sets per 100 people A 124 B 94 C 129 D 109 E 114 A) a. 115 b. 13.69 B) a. 114 b. 13.69 C) a. 114 b. 169 D) a. 113 b. 13.69 Provide an appropriate response. 11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume? A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.

Step-by-step answer

P Answered by PhD

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

$\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}$

$=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69$

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

$X=\mu-2\sigma$

$=100-(2\times 26)\\=100-52\\=48$

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: $X\sim N(150000, 2300^{2})$

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

P(147700

=P(-1

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

$P(X154800)=P(\frac{X-\mu}{\sigma}\frac{154800-150000}{2400})$

$=P(Z2)\\=0.975\\$

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

$z=\frac{x-\mu}{\sigma}$

Mathematics

Find the a. MEAN and b. STANDARD DEVIATION for the data set. Round to two decimal places. 10) Country Number of Television Sets per 100 people A 124 B 94 C 129 D 109 E 114 A) a. 115 b. 13.69 B) a. 114 b. 13.69 C) a. 114 b. 169 D) a. 113 b. 13.69 Provide an appropriate response. 11) If an adult male is told that his height is within 2 standard deviations of the mean of the normal distribution of heights of adult males, what can he assume? A) His height measurement is in the same range as about 99.7% of the other adult males whose heights were measured.

Step-by-step answer

P Answered by PhD

Explained below.

Step-by-step explanation:

(10)

The data set is:

S = {124, 94, 129, 109, 114}

The mean and standard deviation are:

$\bar x=\frac{1}{n}\sum x=\frac{1}{5}\times [124+94+...+114]=114\\\\s=\sqrt{\frac{1}{n-1}\sum ( x-\bar x)^{2}}$

$=\sqrt{\frac{1}{5-1}\times [(124-114)^{2}+(94-114)^{2}+...+(114-114)^{2}]}\\=\sqrt{\frac{750}{4}}\\=13.6931\\\approx 13.69$

The correct option is B.

(11)

According to the Empirical 95% of the data for a Normal distribution are within 2 standard deviations of the mean.

So, the adult male's height is in the same range as about 95% of the other adult males whose heights were measured.

The correct option is B.

(12)

Let the score be X.

Given:

μ = 100

σ = 26

$X=\mu-2\sigma$

$=100-(2\times 26)\\=100-52\\=48$

The correct option is B.

(13)

Let X be the prices of a certain model of new homes.

Given: $X\sim N(150000, 2300^{2})$

Compute the percentage of buyers who paid between $147,700 and $152,300 as follows:

P(147700

=P(-1

According to the 68-95-99.7, 68% of the data for a Normal distribution are within 1 standard deviations of the mean.

The correct option is D.

(14)

Compute the percentage of buyers who paid more than $154,800 as follows:

$P(X154800)=P(\frac{X-\mu}{\sigma}\frac{154800-150000}{2400})$

$=P(Z2)\\=0.975\\$

According to the 68-95-99.7, 95% of the data for a Normal distribution are within 2 standard deviations of the mean. Then the percentage of data above 2 standard deviations of the mean will be 97.5% and below 2 standard deviations of the mean will be 2.5%.

The correct option is D.

(15)

The z-score is given as follows:

$z=\frac{x-\mu}{\sigma}$

Mathematics

Answer questions (a-d) for the following three data sets. a= {3,5,7,9,11,12,12} b= {1,2,2,5,5,9,13} c= { 2,5,8,9,12,13,17} a) find the mean of each data set b) find the standard deviation of each data set c) identify the data set with the largest and smallest standard deviation d) explain what the standard deviations say about the data sets

Step-by-step answer

P Answered by PhD

3

Step-by-step explanation:

Answer questions (a-d) for the following three data sets. a= {3,5,7,9,11,12,12} b= {1,2,2,5,5,9,13}

Mathematics

1.)the data shows the number of grams of fat found in 9 different health bars. 12, 14, 16, 17.5, 10, 18, 15, 15.5, 19 what is the iqr (interquartile range) for the data? 4.75 9 15.5 17.75 2.) what is the range of the data set? 32, 21, 88, 64, 88, 107, 101 3.) lara is calculating the standard deviation of a data set that has 8 values. she determines that the sum of the squared deviations is 184. what is the standard deviation of the data set? round the answer to the nearest tenth. 4.) what is the standard deviation of the data set? 7, 3, 4, 2, 5,

Step-by-step answer

P Answered by PhD

17

Given:

The data shows the number of grams of fat found in 9 different health bars.

12, 14, 16, 17.5, 10, 18, 15, 15.5, 19

The IQR of the data is determined by first arranging the data according to their values, from lowest to highest:

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

IQR = 4.75 = Q3 - Q1

What is the range of the data set?

32, 21, 88, 64, 88, 107, 101

Again, rearrange the data according to value (lowest to highest), then find the minimum and maximum values:

Range = 21 to 107

Mathematics

Select all of the true statements about the standard deviation of a quantitative variable. 1. Standard deviation is resistive to unusual values. 2.The standard deviation of a set of values is equal to 0 if and only if all of the values are the same. 3. Standard deviation is never negative. 4.Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation. 5.If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect

Step-by-step answer

P Answered by Master

Considering the first statement

Standard deviation is resistive to unusual values

This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean

Considering the second statement

The standard deviation of a set of values is equal to 0 if and only if all of the values are the same.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Considering the third statement

Standard deviation is never negative.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Considering the fourth statement

Changing the units of a set of values (e.g., converting from inches to feet) does not affect its standard deviation

This statement is false because standard deviation is the numeric measure of deviation of the each observation from the mean

Considering the fifth statement

If a set of values has a mean of 0 and a standard deviation that is not 0, then adding a new data point with a value of 0 will have no effect on the standard deviation.

This statement is false because , let take an example

x -4 - 3 0 3 4

Generally the mean is mathematically evaluated as

$\= x = \frac{\sum x_i }{n}$

=> $\= x = \frac{-4+ (- 3)+ 0 + 3 + 4 }{5}$

=> $\= x = 0$

Generally the standard deviation is mathematically evaluated as

$\sigma = \sqrt{\frac{\sum (x_ i - \= x )^2}{y} }$

$\sigma = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (0 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{5} }$

=> $\sigma = 3.16$

Now when zero is removed the standard deviation is

$\sigma_1 = \sqrt{\frac{ (-4 - 0 )^2 + (- 3 - 0 )^2 + (3 - 0)^2 + (4 - 0 )^2}{4} }$

=> $\sigma_1 = 3.54$

Since $\sigma \ne \sigma _1$ the above statement is false

Considering the sixth statement

Standard deviation represents how far a group of values are from the mean of those values, on average.

This statement is true because standard deviation is the numeric measure of deviation of the each observation from the mean.

Step-by-step explanation:

Mathematics

1.)the data shows the number of grams of fat found in 9 different health bars. 12, 14, 16, 17.5, 10, 18, 15, 15.5, 19 what is the iqr (interquartile range) for the data? 4.75 9 15.5 17.75 2.) what is the range of the data set? 32, 21, 88, 64, 88, 107, 101 3.) lara is calculating the standard deviation of a data set that has 8 values. she determines that the sum of the squared deviations is 184. what is the standard deviation of the data set? round the answer to the nearest tenth. 4.) what is the standard deviation of the data set? 7, 3, 4, 2, 5,

Step-by-step answer

P Answered by PhD

17

Given:

The data shows the number of grams of fat found in 9 different health bars.

12, 14, 16, 17.5, 10, 18, 15, 15.5, 19

The IQR of the data is determined by first arranging the data according to their values, from lowest to highest:

10, 12, 14, 15, 15.5, 16, 17.5, 18, 19

IQR = 4.75 = Q3 - Q1

What is the range of the data set?

32, 21, 88, 64, 88, 107, 101

Again, rearrange the data according to value (lowest to highest), then find the minimum and maximum values:

Range = 21 to 107

Find the standard deviation of the following set of data

Faq

Try asking the Studen AI a question.