Statistics for Data Science I Qualifier: 7 August 2022 (May 2022 term)

The age of the participants in a dance competition are plotted in a stem and leaf plot as shown in Figure 1.2.Q.

What is the value of population standard deviation of the first 2n natural numbers, i.e. 1, 2, 3, ..., 2n – 2, 2n – 1, 2n?

In the last 5 innings of a school cricket tournament, Manish scored 2, 4, 10, 12, and 14 runs. The population mean and the population variance of the scores of his last 7 innings are 8 and 16 respectively. What are the remaining two scores?

A free mega health checkup is conducted by a clinic at Olympia society. The systolic blood pressure (in mm Hg) of participants is listed in Table 1.1.Q. Calculate the approximate mean value of systolic blood pressure.

Consider various variables that describe the specifications of mobile phones in a store. These variables include the brands, internal storage (in GB), display size (in inches), price (in rupees), support (3G, 4G, 5G), and sim slots (single, dual). The specifications for different mobile phones are listed in a table. Based on the given information, choose the correct statement(s) from the following:

If mean, median, and mode of a numerical variable is the same, then:

Which of the following options represent(s) cross-sectional data? (More than one option could be correct.)

The tax paid by 100 employees of a company is given in a dataset. If the tax details of 200 more employees are added to the same dataset, then which among the following about the range will hold true? (More than one option could be correct)

If the population standard deviation of the first 2n natural numbers (excluding zero) is s1, the population standard deviation of the next 2n natural numbers is s2, and the population standard deviation of the first 4n natural numbers (excluding zero) is s3, then which of the following statements is/are true?

If there are two variables x and y, each having n data points, where each data point is obtained by xi = i, yi = n − i, what is the correlation coefficient of x and y?

The stem and leaf plot of the weights of 10 wrestlers is shown in Figure 1.1.Q.

What is the mean weight (in kg) of the data given in Figure 1.1.Q? (Enter the answer correct to 2 decimal accuracy.)

In an organization, the manager wants to find out the relation between gender and salary earned. He calculated the absolute value of point bi-serial correlation coefficient and found it to be equal to 0.7. In the next quarter, the salary of every employee is tripled. What will be the absolute value of point bi-serial correlation coefficient after the salary is tripled? (Correct up to 1 decimal point accuracy.)

The histogram in Figure 1.4.Q represents the marks distribution of 50 students of college XYZ in their Statistics quiz.

Find the approximate value of mean of the marks scored by students.

In a college, the gender distribution of college faculty is given as stacked bar chart in Figure 1.3.Q. There are three designation for faculty: assistant professor, associate professor, and professor. The total number of assistant professors, associate professors and professors are 250, 100, and 50 respectively. Based on this information, answer the subquestions.

What is the median of faculty designation?

In a college, the gender distribution of college faculty is given as stacked bar chart in Figure 1.3.Q. There are three designation for faculty: assistant professor, associate professor, and professor. The total number of assistant professors, associate professors and professors are 250, 100, and 50 respectively. Based on this information, answer the subquestions.

Choose the correct option(s) from the following statements about the dataset given in Figure 1.3.Q.

Based on the given data, answer the subquestions.

On the basis of the information given in Table 1.2.Q, select the correct statement(s) from the following:

Based on the given data, answer the subquestions.

Identify the correct stack bar chart representing the row relative frequencies of the type of delivery services from Table 1.2.Q.