Question

Math Project Help?

Answer 1

Answer:

Step-by-step explanation:

Hello!

X: Number of chapters per book in the bible.

1.

Mean (X[bar])

X[bar]= ∑X/n= 929/39= 23.82

Median (Me)

To calculate the median you determine its position first, then you have to arrange the data from least to greatest and identify the corresponding value:

Position: (n+1)/2= (39+1)/2= 20

The 20th observation corresponds to the median of this data set:

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

Me= 14

Mode (Md)

The mode corresponds to the value with the most observed frequency, in this case, if we are studying the numbers of chapters per book so the mode will correspond to the "number of chapters" that is most repeated.

Once again you have to arrange the data from least to greatest.

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

"3 chapters" is repeated 4 times

"4 chapters" is repeated 4 times

"10 chapters" is repeated 2 times

"12 chapters" is repeated 2 times

"14 chapters" is repeated 2 times

"24 chapters" is repeated 2 times

"31 chapters" is repeated 2 times

"36 chapters" is repeated 2 times

This data set has two modes Md₁= 3 and Md₂= 4 and its called "bimodal" distribution.

Range (R)

The range of the distribution is the difference between the maximum and minimum values of the data set:

Minimum: 1 chapter

Maximum: 150 chapters

R=max-min= 150-1= 149

2.

Out of the 5 number summary, I've already identified three: Min, Max, and Me.

To calculate the first (Q₁) and third (Q₃) quartiles you have to calculate their positions first and then identify them in the data set (arranged from least to greatest)

PosQ₁= (n+1)/4= 40/4= 10

PosQ₃= (n+1)*3/4= 40*3/4= 30

1 2 3 3 3 3 4 4 4 5 7 8 9 10 10 12 12 13 14 14 21 22 24 24 25 27 29 31 31 34 36 36 40 42 48 50 52 66 150

Q₁= 5

Q₃= 34

3. Box plot attached.

4. Histogram attached

5.

a. and d.

An outlier is an observation that is significantly distant from the rest of the data set. They usually represent experimental errors (such as a measurement) or atypical observations. Some statistical measurements, such as the sample mean, are severely affected by this type of values and their presence tends to cause misleading results on statistical analysis.

Considering the 1st quartile (Q₁), the 3rd quartile (Q₃) and the interquartile range IQR, any value X is considered an outlier if:

X < Q₁ - 1.5 IQR

X > Q₃ + 1.5 IQR

Or extreme outliers if:

X < Q₁ - 3 IQR

X > Q₃ + 3 IQR

Q₁= 5

Q₃= 34

IQR= Q₃ - Q₁= 34 - 5= 29

Limits for outliers:

Q₁ - 1.5 IQR = 5-(1.5*29)= -38.5

Q₃ + 1.5 IQR = 34+(1.5*29)= 77.5

Limits for extreme outliers:

Q₁ - 3 IQR = 5 - (3*29)= -82

Q₃ + 3 IQR= 34 + (3*29)= 121

As you can see, comparing the data with the criteria to classify a value as an outlier, there is only one in the data set and, since it is more than 3 IQR away from the third quartile, it is an extreme outlier: 150 chapters

b. and c.

Central tendency measures:

X[bar]= 23.82 ⇒ the mean or average number is also known as the "expected" value of the distribution. This measurement is always a value within the range of definition of the variable but does not necessarily coincide with an observation. Another characteristic of this measurement is that it is greatly affected by outliers and tends to "move" its position towards them.

You can say that on average the books of the bible have 23.82 chapters

If you take the outlier out of the data set and calculate the mean, you'd expect it to be less and closer to the median:

X[bar] (without 150):∑X/n= 779/38= 20.5

Md₁= 3 and Md₂= 4 ⇒ Both modes are on the lower end of the distribution, aside for showing that there are many books with the same amount of chapters, it shows no more information.

Me= 14 ⇒ The median is the value that separates the distribution in halves, considering that there is an outlier that affects the value of the mean, is the median the measure that best describes the distribution.

I hope this helps!