Comprehension
Read the scenario and answer the question:
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2.
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values:
Minimum: 2
Lower Hinge: 6.5
Median: 12
Upper Hinge: 21
Maximum: 29
The upper hinge of a dataset is the median of all the values to the right of the median of the dataset in an ascending arrangement, while the lower hinge of the dataset is the median of all the values to the left of the median of the dataset in the same arrangement.
For example, consider the dataset 4, 3, 2, 6, 4, 2, 7. When arranged in the ascending order, it becomes 2, 2, 3, 4, 4, 6, 7. The median is 4 (the bold value), and hence the upper hinge is the median of 4, 6, 7, i.e., 6. Similarly, the lower hinge is 2.
A student has surveyed thirteen of her teachers, and recorded their work experience (in integer years). Two of the values recorded by the student got smudged, and she cannot recall those values. All she remembers is that those two values were unequal, so let us write them as A and B, where A < B. The remaining eleven values, as recorded, are: 5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29. Moreover, the student also remembers the following summary measures, calculated based on all the thirteen values:
Minimum: 2
Lower Hinge: 6.5
Median: 12
Upper Hinge: 21
Maximum: 29
Question: 1
Which of the following is a possible value of B?
Which of the following is a possible value of B?
Updated On: Aug 9, 2024
- 2
- 6
- 8
- 13
- 29
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
The Correct Option is (C):8
Was this answer helpful?
0
0
Question: 2
Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
Based on the information recorded, which of the following can be the average work experience of the thirteen teachers?
Updated On: Dec 5, 2024
- 12
- 12.5
- 13
- 13.5
- 14
Hide Solution
Verified By Collegedunia
The Correct Option is
Solution and Explanation
Step 1: Calculate the total sum of the dataset. The average is given by:
Average = $\frac{\text{Sum of all values}}{\text{Total number of values}}$.
Let A and B represent the smudged values, where A + B = 18 (from Question 20). The eleven known values are:
5, 6, 7, 8, 12, 16, 19, 21, 21, 27, 29.
The sum of the eleven known values:
5 + 6 + 7 + 8 + 12 + 16 + 19 + 21 + 21 + 27 + 29 = 171.
Step 2: Calculate the total sum with A and B. The total sum is:
Total Sum = 171 + A + B = 171 + 18 = 189.
Step 3: Calculate the average.
Average = $\frac{189}{13} = 13$.
Final Answer: 13.
Was this answer helpful?
0
0
Question: 3
While rechecking her original notes to re-enter the smudged values of A and B in the records, the student found that one of the eleven recorded work experience values that did not get smudged was recorded wrongly as half of its correct value. After re-entering the values of A and B, and correcting the wrongly recorded value, she recalculated all the summary measures. The recalculated average value was 15.
What is the value of B?
While rechecking her original notes to re-enter the smudged values of A and B in the records, the student found that one of the eleven recorded work experience values that did not get smudged was recorded wrongly as half of its correct value. After re-entering the values of A and B, and correcting the wrongly recorded value, she recalculated all the summary measures. The recalculated average value was 15.
What is the value of B?
What is the value of B?
Updated On: Dec 5, 2024
- 7
- 9
- 10
- 12
- Cannot be determined from the given information.
Hide Solution
Verified By Collegedunia
The Correct Option is C
Solution and Explanation
Step 1: Determine the total recalculated sum. The recalculated average is 15. Using the formula for average:
Average = $\frac{\text{Sum of all values}}{\text{Total number of values}}$
15 = $\frac{\text{Recalculated Total Sum}}{13}$
Thus:
Recalculated Total Sum = 15 × 13 = 195.
Step 2: Calculate the correction applied. The original sum of the eleven known values was 171. After adding A and B, the total becomes:
171 + A + B = 171 + 18 = 189.
The recalculated total sum is 195, so the difference due to the correction is:
195 − 189 = 6.
This means one of the recorded values was half of its correct value. Let the wrongly recorded value be x. Then:
$\frac{x}{2}$ + 6 = x = => x = 12.
Step 3: Solve for B. From Question 20, A + B = 18. If A = 6, then:
B = 18 − 6 = 9.
Final Answer: 9.
Was this answer helpful?
0
0
Top Questions on Data Interpretation
- The bar chart gives the batting averages of VK and RS for 11 calendar years from 2012 to 2022. Considering that 2015 and 2019 are world cup years, which one of the following options is true?
- GATE CE - 2024
- General Aptitude
- Data Interpretation
The above is a schematic diagram of walkways (indicated by all the straight-lines) and lakes (3 of them, each in the shape of rectangles – shaded in the diagram) of a gated area. Different points on the walkway are indicated by letters (A through P) with distances being OP = 150 m, ON = MN = 300 m, ML = 400 m, EL = 200 m, DE = 400 m.
The following additional information about the facilities in the area is known.
1. The only entry/exit point is at C.
2. There are many residences within the gated area; all of them are located on the path AH and ML with four of them being at A, H, M, and L.
3. The post office is located at P and the bank is located at B.- CAT - 2024
- Data Interpretation & Logical Reasoning (DILR)
- Data Interpretation
- Two students, Amiya and Ramya are the only candidates in an election for the position of class representative. Students will vote based on the intensity level of Amiya’s and Ramya’s campaigns and the type of campaigns they run. Each campaign is said to have a level of 1 if it is a staid campaign and a level of 2 if it is a vigorous campaign. Campaigns can be of two types, they can either focus on issues, or on attacking the other candidate.
If Amiya and Ramya both run campaigns focusing on issues, then
• The percentage of students voting in the election will be 20 times the sum of the levels of campaigning of the two students. For example, if Amiya and Ramya both run vigorous campaigns, then $20 × (2+2)\%$, that is, $80\%$ of the students will vote in the election.
• Among voting students, the percentage of votes for each candidate will be proportional to the levels of their campaigns. For example, if Amiya runs a staid (i.e., level 1) campaign while Ramya runs a vigorous (i.e., level 2) campaign, then Amiya will receive \(\frac{1}{3}\) of the votes cast, and Ramya will receive the other \(\frac{2}{3}\).
The above-mentioned percentages change as follows if at least one of them runs a campaign attacking their opponent.
• If Amiya runs a campaign attacking Ramya and Ramya runs a campaign focusing on issues, then $10\%$ of the students who would have otherwise voted for Amiya will vote for Ramya, and another $10\%$ who would have otherwise voted for Amiya, will not vote at all.
• If Ramya runs a campaign attacking Amiya and Amiya runs a campaign focusing on issues, then $20\%$ of the students who would have otherwise voted for Ramya will vote for Amiya, and another $5\%$ who would have otherwise voted for Ramya, will not vote at all.
• If both run campaigns attacking each other, then $10\%$ of the students who would have otherwise voted for them had they run campaigns focusing on issues, will not vote at all.- CAT - 2024
- Data Interpretation & Logical Reasoning (DILR)
- Data Interpretation
- Read the Passage carefully and answer the following questions.
An air conditioner (AC) unit has three operating modes: Eco, Normal, and Turbo. The power consumption in each mode is as follows: Eco mode consumes 1000 watts, Normal mode consumes 1200 watts, and Turbo mode consumes 1500 watts. Yesterday, the AC was in operation from 2 PM to 10 PM. From 2 PM to 6 PM it ran in Eco mode. From 6 PM to 8 PM, it ran in Normal mode. From 8 PM to 10 PM it ran in Turbo mode.- CAT - 2024
- Data Interpretation & Logical Reasoning (DILR)
- Data Interpretation
- Read the Passage carefully and answer the following questions
A health food store specializing in dietary supplements and whole grains recorded the following sales figures (in kilograms) for various food categories last month: Millets (M) = 500 kg at a cost price of 40/kg and selling price of 50/kg; Protein supplements (P) = 300 kg at a cost price of 80/kg and selling price of 100/kg; Vitamin supplements (V) = 200 kg at a cost price of 60/kg and selling price of 80/kg; Carbohydrates (C) = 600 kg at a cost price of 80/kg and selling price of 100/kg; Fats (F) = 100 kg at a cost price of 120/kg and selling price of 150/kg. Additionally, they sold 50 kg of mixed nuts (N) at a cost price of 100/kg and a selling price of 130/kg- CAT - 2024
- Data Interpretation & Logical Reasoning (DILR)
- Data Interpretation
View More Questions
Questions Asked in XAT exam
- Arya, a graduate from a reputable institute, got a job in an IT company but became bored after a year. Her best friend S, who worked at the same company, joined a top-tier B-school for an MBA, which tempted Arya to pursue the same path. Her friend assured her that an MBA would boost her career prospects and salary. Arya started preparing for an MBA while continuing her job, but the challenge of balancing preparation with work made her consider leaving the job.
- XAT - 2025
- Analytical Decision Making
- There’s a community 30 km outside of the main city. Mr. S started a grocery business in the community after winning the bid by offering way above the rent initially drafted by the community council. The community council, led by Mr. D, agreed to the offer with a performance review every three years. Mr. S also agreed to provide an additional 15% of his grocery sales to the council, banking on the prospect of selling in higher volumes. After setting up his business, Mr. S noticed that SUV owners in the community usually bought goods in bulk from the city once a week and used his store primarily for daily necessities and occasional big purchases like mixer grinders.
- XAT - 2025
- Analytical Decision Making
- Four reviewers (R1, R2, R3, R4) are in charge of reviewing products from companies A, B, C, and D. Each reviewer provides a rating between 1 and 5 for the products. Due to a technical glitch, the original ratings were deleted, and only the averages calculated for each product (A, B, C, D) and each reviewer (R1, R2, R3, R4) were saved. The data available is as follows:Tasks:
A B C D Average 3 4 4 ? 4 3 ? 5 ? 4 ? 3 3 ? 4 ? ? ? ? 4.25 4 4 4 4.25
1. What are the missing values in the table?
2. How were the missing values calculated?
3.Verify the correctness of the given averages for both rows and columns. - In an 8-week course, the teacher conducts a test every week, and the scores are in the range of 1–4. There are only two students enrolled in the course, \(R\) and \(S\). The following conditions are given:
- \(R\) and \(S\) scored the same on the first test.
- From the second test onwards, \(R\) consistently scored the same (a non-zero score).
- The total of the first three test scores of \(R\) equals the total of the first two test scores of \(S\).
- From the fifth test onwards, \(S\) scored the same as \(R\).
- The scores of \(S\) from the first two tests and all the remaining tests follow a geometric progression.
- XAT - 2025
- Algebra
- A bought a phone from a store and paid \(\frac{1}{6}\) of the price using UPI, \(\frac{1}{3}\) of the price in cash, and the remaining balance a year later. He also paid 10% interest on the remaining balance after one year. What was the original price of the phone?
- XAT - 2025
- Percentage
View More Questions