Question

An entrepreneur faces many bureaucratic and legal hurdles when starting a new business. The World Bank collects information about starting businesses throughout the world. They have determined the time, in days, to complete all of the procedures required to start a business. The data for business start time, in days, for a sample of 24 countries is given. Data Set
13 66 36 12 8 27 6 7 5 7 52 48
15 7 12 94 28 5 13 60 5 5 18 18
The total for the given data is 567 days.
Later, we realize that we had not included the data for the South American country of Suriname in the sample. The start time for Suriname is 694 days.
a) What is the mean of the sample data including the country of Suriname? Give your answer to two decimal place.
b) Find the median time to start a business for 24 countries in our data set:
c) Which measure do you prefer for describing the center of this distribution? Explain your answer.
d) Compute the quartiles (Q1, Q2, Q3), and find the IQR for these data. Are there outliers in the time to start a business data set? If so, identify and name any outliers.
e) Compute the standard deviation of time to start a business for 24 countries in the data set:
f) Which measure do you prefer for describing the spread of this distribution? Explain your answer.
g) Make a boxplot for these data and explain & describe the distribution using only the information in the boxplot.

Answer 1

Answer:

Kindly check explanation

Step-by-step explanation:

Given the data :

Rearranged data:

5, 5, 5, 5, 6, 7, 7, 7, 8, 12, 12, 13, 13, 15, 18, 18, 27, 28, 36, 48, 52, 60, 66, 94

Start time for Suriname = 694

Mean = ΣX / n

Mean = (567 + 694) / (24 + 1) = 1261 / 25 = 50.44

B.) median start Time for initial 24 values

0.5(n+1)th term

0.5(25) = 12.5th term

(13 + 13) / 2 = 13

C.) preferred measure of center for the distribution will be the median as it shapes well in the middle of the distribution. The mean is overestimated

d) Compute the quartiles (Q1, Q2, Q3), and find the IQR for these data. Are there outliers in the time to start a business data set? If so, identify and name any outliers.

Using calculator :

Lower quartile Q1 --> 7

Median Q2 --> 13

Upper quartile Q3 --> 42

IQR = (Q3 - Q1) = 42 - 7 = 35

OUTLIER:

Lower bound : Q1 - 1.5(IQR) ; 7 - 1.5(35) = - 45.5

Upper bound : Q3 + 1.5(IQR) = 42 + 1.5(35) = 94.5

Outlier : values below - 45.5 and above 94.5

Hence, Surimanes start time is the only Outlier.

e)

Standard deviation for 24 countries :

Standard deviation = sqrt[Σ(X - mean)^2 / (N - 1)]

Usibg calculator :

Standard deviation for the 24 countries is 23.83

f)

Standard deviation