Statistics (सांख्यिकी) MCQ Test — Class 9 Maharashtra SSC

Solution:

Primary data refers to data collected by the investigator himself/herself for a specific purpose directly from the source.

When a class teacher conducts a test and records the marks, they are collecting this data firsthand, making it primary data.

Options A, B, and D describe data that has already been collected, compiled, or published by others, which falls under secondary data.

Solution:

Raw data is data that has not been processed, organized, or analyzed in any way.

It is the initial form in which data is collected directly from the source.

Arrayed data is raw data arranged in ascending or descending order, while grouped data is organized into classes or intervals.

Solution:

The frequency of an observation or category is simply the count of how many times it appears or occurs in the data set.

In this scenario, 'Cricket' was chosen by 8 students.

Therefore, the frequency of 'Cricket' is 8.

Solution:

The given class interval is 10-19. This is an inclusive class interval, meaning all values from 10 up to and including 19 are part of this class.

The formula for the class size of an inclusive interval is (Upper Limit - Lower Limit + 1).

Applying the formula: Class size = (19 - 10 + 1) = 9 + 1 = 10.

Solution:

The class mark is the representative value of a class interval.

It is calculated as the average of the upper and lower limits of the class interval.

Formula: Class Mark = (Lower Limit + Upper Limit) / 2. This definition makes it the midpoint.

Solution:

One of the properties of the mean is that if each observation in a data set is increased by a constant value 'k', the new mean will be the old mean plus 'k'.

Given the original mean = 20 and the constant increase 'k' = 5.

New Mean = Original Mean + k = 20 + 5 = 25.

Solution:

To find the median of ungrouped data, the observations must first be arranged in either ascending or descending order.

Ria directly picked the third number from the given unordered list, which is incorrect.

The correct ordered data is: 18, 22, 25, 28, 30. For an odd number of observations (5 in this case), the median is the middle value, which is the 3rd term, 25.

Solution:

The mode is defined as the observation that occurs most frequently in a data set (Statement C is TRUE).

A data set can indeed have more than one mode (e.g., bimodal, trimodal) if multiple observations share the highest frequency. For example, in {1, 2, 2, 3, 3, 4}, both 2 and 3 are modes (Statement A is TRUE).

Therefore, the statement 'The mode is always unique' is FALSE.

The mode can also be found for qualitative data (e.g., the most popular color in a survey) (Statement D is TRUE).

Solution:

In discontinuous class intervals (also known as inclusive intervals), there is a gap between the upper limit of one class and the lower limit of the next class.

For example, between 5-9 and 10-14, the gap is (Lower limit of next class - Upper limit of current class) = 10 - 9 = 1.

The correction factor is calculated as half of this gap: Correction Factor = Gap / 2 = 1 / 2 = 0.5.

This factor is subtracted from lower limits and added to upper limits to create continuous (exclusive) intervals.

Solution:

The average (mean) score of 5 students is 18.

The total sum of their scores = Mean × Number of students = 18 × 5 = 90.

The sum of the scores of the four given students = 15 + 20 + 16 + 19 = 70.

Let the score of the fifth student be 'x'. Then, the total sum of scores is 70 + x. So, 70 + x = 90. Solving for x, we get x = 90 - 70 = 20.