Mathematics, 07.04.2020 03:27 KillerSteamcar

Given the data

0.90 1.32 1.96 1.85 2.29 1.42 1.35 1.47 1.74 1.82 1.30 1.47 1.92
1.65 2.06 1.55 1.95 1.35 1.78 1.63 1.66 1.05 1.71 2.14 1.27

Determine the (a) mean, (b) median, (c) mode, (d) range, (e) standard deviation, (f) variance, and (g) coefficient of variation. Construct a histogram from the data using a range from 0.8to 2.4with intervals of 0.2

Answers: 2

Show answers

Answers

Answer from: minervica

(a) Mean = 1.6244 (b) Median = 1.65

(e) Standard deviation = 0.3325

(f) Variance = 0.1106

(g) Coefficient of variation = 20.47%.

Step-by-step explanation:

The mean (μ) of a data set is the average value of the data set. The formula to compute mean is:

$\mu=\frac{1}{n}\sum X_{i}$

The median (m) is a quantity in statistics that points out where the mid-value of a data set is. In case of, odd number of data-values, the median is given by,

$Median=(\frac{n+1}{2})^{th}\ obs.$

The mode (M) of a data set is the value that appears most often.

The range of a data-set is the difference between the maximum and minimum values in the data-set.

Range=Max.-Min.

The standard deviation of a data set is a numerical value that represents the amount of variation between the observed values.

$SD=\sqrt{\frac{1}{n-1}\sum (X_{i}-\mu)^{2}}$

The variance is the square of the standard deviation.

$Var=\frac{1}{n-1}\sum (X_{i}-\mu)^{2}$

The coefficient of variation (CV) is well defined as the ratio of the standard deviation to the mean. It exhibits the degree of variation in association to the mean of the population.

The formula to compute the coefficient of variation is,

$CV=\frac{\sigma}{\mu}\times 100\%$

Consider the data set provided.

(a)

Compute the mean as follows:

$\mu=\frac{1}{n}\sum X_{i}=\frac{1}{25}\times 40.61=1.6244$

Thus, the mean of the data is 1.6244.

(b)

Compute the median as follows:

Arrange the data in ascending order as follows:

0.9 , 1.05 , 1.27 , 1.3 , 1.32 , 1.35 , 1.35 , 1.42 , 1.47 , 1.47 , 1.55 , 1.63 , 1.65 ,

1.66 , 1.71 , 1.74 , 1.78 , 1.82 , 1.85 , 1.92 , 1.95 , 1.96 , 2.06 , 2.14 , 2.29

$Median=(\frac{n+1}{2})^{th}\ obs.=(\frac{25+1}{2})^{th}\ obs.=13^{th}\ obs.=1.65$

Thus, the median of the data set is 1.65.

(c)

Compute the mode as follows:

Consider the data arranged in ascending order above.

0.9 , 1.05 , 1.27 , 1.3 , 1.32 , 1.35 , 1.35 , 1.42 , 1.47 , 1.47 , 1.55 , 1.63 , 1.65 ,

1.66 , 1.71 , 1.74 , 1.78 , 1.82 , 1.85 , 1.92 , 1.95 , 1.96 , 2.06 , 2.14 , 2.29

The value 1.35 repeats twice and none of the other values repeat themselves.

Thus, the mode of the data set is 1.35.

(d)

Compute the range as follows:

$Range=Max.-Min.\\=2.29-0.90\\=1.39$

Thus, the range of the data set is 1.39.

(e)

Compute the standard deviation as follows:

$SD=\sqrt{\frac{1}{n-1}\sum (X_{i}-\mu)^{2}}=\sqrt{\frac{1}{25-1}\sum (X_{i}-1.6244)^{2}}=0.3325$

Thus, the standard deviation is 0.3325.

(f)

Compute the variance as follows:

$Var=(SD)^{2}=(0.3325)^{2}=0.1106$

Thus, the variance is 0.1106.

(g)

Compute the coefficient of variation as follows:

$CV=\frac{\sigma}{\mu}\times 100\%=\frac{0.3325}{1.6244}\times 100\%=20.47\%$

Thus, the coefficient of variation is 20.47%.

The histogram is attached below.

Given the data 0.90 1.32 1.96 1.85 2.29 1.42 1.35 1.47 1.74 1.82 1.30 1.47 1.92 1.65 2.06 1.55 1.9

Answer from: Quest

step-by-step explanation:

if you meant, "on the way from (3, 2) to (3, 14):

x does not change; y increases by 12.

ensure that you have copied down this problem correctly. .

Answer from: Quest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.

Another question on Mathematics

Mathematics, 21.06.2019 16:30

How do you summarize data in a two-way frequency table?

Answers: 3

Answer

Mathematics, 21.06.2019 19:40

Afactory makes propeller drive shafts for ships. a quality assurance engineer at the factory needs to estimate the true mean length of the shafts. she randomly selects four drive shafts made at the factory, measures their lengths, and finds their sample mean to be 1000 mm. the lengths are known to follow a normal distribution whose standard deviation is 2 mm. calculate a 95% confidence interval for the true mean length of the shafts. input your answers for the margin of error, lower bound, and upper bound.

Answers: 3

Answer

Mathematics, 21.06.2019 22:00

Find the maximum value of p= 4x + 5y subject to the following constraints :

Answers: 3

Answer

Mathematics, 21.06.2019 22:30

Which set of lengths could represent the sides of a triangle? a. 3, 7, 10 b. 4, 5, 10 c. 6, 8, 14 d. 12, 6, 7

Answers: 1

Answer

You know the right answer?

Given the data

0.90 1.32 1.96 1.85 2.29 1.42 1.35 1.47 1.74 1.82 1.30 1.47 1.92
...