Read the given passage and answer the questions that follow The following table has the number of enrolled students for a particular course and year. Total number of seats are given in brackets with respect to each course. Number of Enrolled Students BTech MTech MPhilYear
(120)
(30)
(20)MBA
(60)2016 96 24 12 52 2017 110 26 14 57 2018 108 25 13 54 2019 112 28 15 56 2020 104 27 16 48
What is the average number of vacant seats of B. Tech for years (2016-2020)?
14
Understanding the Question: Calculating Average Vacant B.Tech Seats
The question asks us to find the average number of vacant seats in the B.Tech course over a specific period, from the year 2016 to 2020. We are given a table containing the number of students enrolled in various courses each year, including B.Tech, and the total capacity (number of seats) for each course.
Data Analysis: Extracting B.Tech Information
First, let's identify the relevant data for the B.Tech course from the provided table. The total number of seats for B.Tech is fixed at 120 for all years. The number of enrolled students varies each year:
| Year | B.Tech Total Seats | B.Tech Enrolled Students |
|---|---|---|
| 2016 | 120 | 96 |
| 2017 | 120 | 110 |
| 2018 | 120 | 108 |
| 2019 | 120 | 112 |
| 2020 | 120 | 104 |
Calculating Vacant Seats for Each Year
The number of vacant seats for any given year is calculated by subtracting the number of enrolled students from the total number of seats.
\(\text{Vacant Seats} = \text{Total Seats} - \text{Enrolled Students}\)
Let's calculate the vacant seats for B.Tech for each year from 2016 to 2020:
- 2016: \(120 - 96 = 24\) vacant seats
- 2017: \(120 - 110 = 10\) vacant seats
- 2018: \(120 - 108 = 12\) vacant seats
- 2019: \(120 - 112 = 8\) vacant seats
- 2020: \(120 - 104 = 16\) vacant seats
Calculating Total Vacant Seats (2016-2020)
To find the total number of vacant B.Tech seats over the five years, we sum up the vacant seats calculated for each year:
\(\text{Total Vacant Seats} = 24 + 10 + 12 + 8 + 16\)
\(\text{Total Vacant Seats} = 70\)
Calculating the Average Number of Vacant B.Tech Seats
The average number of vacant seats is found by dividing the total number of vacant seats by the number of years considered. In this case, the period is from 2016 to 2020, which includes 5 years.
\(\text{Average Vacant Seats} = \frac{\text{Total Vacant Seats}}{\text{Number of Years}}\)
\(\text{Average Vacant Seats} = \frac{70}{5}\)
\(\text{Average Vacant Seats} = 14\)
Therefore, the average number of vacant seats for B.Tech for the years 2016-2020 is 14.
Summary of Steps
- Identify the total seats and enrolled students for B.Tech each year (2016-2020).
- Calculate vacant seats for each year by subtracting enrolled from total seats.
- Sum the vacant seats over the five years.
- Divide the total vacant seats by 5 (the number of years) to find the average.
Revision Table: B.Tech Seat Data (2016-2020)
| Year | Total Seats | Enrolled Students | Vacant Seats |
|---|---|---|---|
| 2016 | 120 | 96 | 24 |
| 2017 | 120 | 110 | 10 |
| 2018 | 120 | 108 | 12 |
| 2019 | 120 | 112 | 8 |
| 2020 | 120 | 104 | 16 |
| Total Vacant Seats: | 70 | ||
Additional Information: Average Calculation Explained
The average (or arithmetic mean) is a central value of a set of numbers. It is calculated by summing all the numbers in the set and then dividing by the count of those numbers. In this problem, the set of numbers is the annual vacant B.Tech seats (24, 10, 12, 8, 16), and the count is 5 years. Averages are frequently used in data interpretation to understand typical values or trends over a period.
Understanding how to calculate averages and interpret data from tables is a crucial skill for quantitative aptitude sections in many exams.
Important Questions from Data Interpretation
The table given below shows the earnings of two persons on five different days.
What is the ratio of total earnings of P to the total earnings of Q?Earnings Days P Q Monday 105 150 Tuesday 96 110 Wednesday 65 122 Thursday 115 106 Friday 130 68 The table below shows the number of toys of 6 different colours sold from a shop during a given period. The table also shows the percentage of toys of each colour which are cars.
Colour Total toys Percentage of cars C1 500 12 C2 600 15 C3 400 12.5 C4 550 10 C5 650 20 C6 450 10 What is the total number of car toys of C2 and C3 taken together?
Study the given graph carefully and answer the question that follows. The graph shows the demand and production of different companies.
The ratio between the companies having more production than demand and more demand than production is:
Study the given table and answer the question that follows. The given table shows the number of new employees added to different categories of employees in a company for four years and the number of employees from these categories who left the company every year.
During the period between 2001 and 2004, the total number of Technicians who left the Company is what percentage (rounded off to the nearest integer) of the total number of Technicians who joined the Company?
The given pie-chart shows the percentage distribution of 20,000 employees in a company. Study the given chart and answer the question that follows. If 30% of the employees in department D are females, then how many male employees are there in that department?
