Internal Assessment / Mathematics Test
Statistics & Probability
| Class Interval | Frequency |
|---|---|
| 0 - 100 | 2 |
| 100 - 200 | 5 |
| 200 - 300 | x |
| 300 - 400 | 12 |
| 400 - 500 | 17 |
| 500 - 600 | 20 |
| 600 - 700 | y |
| 700 - 800 | 9 |
| 800 - 900 | 7 |
| 900 - 1000 | 4 |
| Total |
SECTION D — Case-Based/Source-Based Integrated Questions [4 Marks Each]
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4 Marks
Q1. Case Study: Traffic Accident Analysis
To judge the accuracy of complaints regarding accidents on a dangerous highway turn, the transport department recorded the number of accidents on that spot for 100 periods, each of 3 minutes duration. The data is summarized below: Number of Accidents 0–10 10–20 20–30 30–40 40–50 50–60 60–70 70–80 Frequency (Number of periods) 7 14 13 12 20 11 15 8
a) Identify the median class of the distribution. (1 Marks)
b) Find the sum of the upper limit of the median class and the lower limit of the modal class. (1 Marks)
c) Calculate the mode of the given data. (2 Marks)
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4 Marks
Q2. Case Study: Weekly Household Electricity Consumption
A local electricity board conducted a survey on the power consumption of families in Colony A. The survey recorded the weekly consumption (in units) of 56 families, structured into the following frequency table: Weekly Consumption (units) 0–10 10–20 20–30 30–40 40–50 50–60 Number of Families 16 12 18 6 4 0
a) Determine the modal class for the weekly electricity consumption (1 Marks)
b) Find the cumulative frequency (cf) corresponding to the class interval just greater than $\frac{N}{2}$ (1 Marks)
c) Calculate the median weekly electricity consumption for the families. (2 Marks)
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4 Marks
Q3. Case Study: Missing Frequencies in Online Classes
During an online mathematics class assignment, a student was analyzing a grouped frequency distribution where two frequency values ( $x$ and $y$) were missing. The total frequency was given as $N = 229$ and the median of the data was recorded as $46$. The table is structured as follows: Class Interval 10–20 20–30 30–40 40–50 50–60 60–70 70–80 Frequency 12 30 $x$ 65 $y$ 25 18
a) State the median class based on the given median value of $46$ (1 Marks)
b) Find the relation between the missing frequencies $x$ and $y$ using the total frequency $N = 229$. (1 Marks)
c) Calculate the precise values of the missing frequencies $x$ and $y$. (2 Marks)
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4 Marks
Q4. Case Study: Hospital Patient Age Distribution
During a medical health camp analysis, a hospital recorded the age distribution of patients admitted on a specific day: Age (in years) 15–25 25–35 35–45 45–55 55–65 65–75 Number of Patients 6 11 21 23 15 4
a) Write the age group that represents the modal class (1 Marks)
b) Calculate the modal age of the patients. (1 Marks)
c) Find the mean age of the patients admitted to the hospital using the direct or assumed mean method. (2 Marks)
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4 Marks
Q5. Case Study: Daily Distance Traveled by Public Buses
To evaluate environmental impact and plan electric bus replacements, a transport department recorded the daily distance traveled by 50 existing public transport buses: Daily Distance (in km) 100–120 120–140 140–160 160–180 180–200 Number of Buses 12 14 8 6 10
a) Determine the class interval that contains the median distance. ( (1 Marks)
b) Calculate the median distance traveled by a bus. ( (1 Marks)
c) Calculate the mean daily distance traveled by a bus. (2 Marks)
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4 Marks
Q6. Case Study: Daily Pocket Expenses of Teenagers
A survey was conducted by a youth club on the daily pocket expenses of 50 teenagers in a locality to understand their saving habits. The data is recorded below: Pocket Expenses (in ₹) 100–120 120–140 140–160 160–180 180–200 Number of Teenagers 12 14 8 6 10
a) Find the class mark of the modal class (1 Marks)
b) Calculate the lower limit of the median class. (1 Marks)
c) Find the empirical mean pocket expense if the mode is recorded at ₹136 and median at ₹142. (2 Marks)
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4 Marks
Q7. Case Study: Plant Sapling Growth Tracking
As part of an environmental project, students of a school measured the height of 60 plant saplings grown under a special organic fertilizer after 30 days: Height (in cm) 0–10 10–20 20–30 30–40 40–50 50–60 Number of Saplings 5 10 18 15 8 4
a) Determine the cumulative frequency of the class preceding the median class (1 Marks)
b) Calculate the median height of the plant saplings (2 Marks)
c) What percentage of plants have a height of less than 30 cm? (1 Marks)
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4 Marks
Q8. Case Study: Daily Production of Ball Bearings
An automated factory produces steel ball bearings. A quality control unit checked the weight of 100 components sampled randomly: Weight (in grams) 40–45 45–50 50–55 55–60 60–65 65–70 Number of Bearings 10 18 25 22 15 10
a) Identify the modal weight category (modal class). (1 Marks)
b) Using the direct or step-deviation method, find the average (mean) weight of a ball bearing. (2 Marks)
c) State the sum of the lower limits of both the median class and modal class (1 Marks)
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4 Marks
Q9. Case Study: Consumer Price Index (CPI) Survey
In an economic evaluation, the monthly grocery expenditure of families in a housing society was compiled into a frequency distribution: Monthly Expenditure (in ₹ thousand) 1–3 3–5 5–7 7–9 9–11 Number of Families 6 9 12 8 5
a) Find the class size ( $h$) of this distribution. (1 Marks)
b) Calculate the modal expenditure for these families. (2 Marks)
c) If every family's monthly expenditure increases uniformly by ₹1,000, what will be the effect on the new mean expenditure? (1 Marks)
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4 Marks
Q10. Case Study: Cricket Match Performance Analysis
The runs scored by a batsman in 40 international innings are summarized below: Runs Scored 0–20 20–40 40–60 60–80 80–100 Number of Innings 6 13 f 5 4
a) If the total number of innings is 40, find the missing frequency $f$. (1 Marks)
b) Determine the class interval where the median runs lie (1 Marks)
c) Calculate the median number of runs scored by the batsman. (2 Marks)
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4 Marks
Q11. Case Study: Water Consumption Survey in Apartments
To manage municipal water distribution efficiently, a housing society recorded the daily water consumption (in liters) of 60 households: Water Consumption (liters) 1000–1500 1500–2000 2000–2500 2500–3000 3000–3500 Number of Households 8 15 22 10 5
a) Write the lower limit of the modal class of this distribution. (1 Marks)
b) Determine the cumulative frequency of the class interval preceding the median class (1 Marks)
c) Calculate the median water consumption per household. (2 Marks)
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4 Marks
Q12. Case Study: School Library Book Usage
The librarian of a high school recorded the number of reference books borrowed by students over a month: Books Borrowed 0–5 5–10 10–15 15–20 20–25 Number of Students 10 15 25 12 8
a) Find the class mark of the median class. (1 Marks)
b) Calculate the modal number of books borrowed by a student. (2 Marks)
c) What is the total number of students surveyed? (1 Marks)
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4 Marks
Q13. Case Study: Smartphone Battery Life Testing
A tech-consumer forum tested the continuous battery backup time (in hours) of 80 budget smartphones under standard usage: Battery Life (hours) 10–15 15–20 20–25 25–30 30–35 Number of Phones 7 19 28 18 8
a) Identify the class interval with the highest frequency. (1 Marks)
b) Calculate the mean battery life using the direct or assumed mean method. (2 Marks)
c) Find the upper limit of the median class. (1 Marks)
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4 Marks
Q14. Case Study: Agricultural Yield Analysis
An agricultural cooperative inspected the wheat yield (in quintals per acre) across 50 farms in a rural district: Yield (quintals/acre) 30–40 40–50 50–60 60–70 70–80 Number of Farms 5 12 18 10 5
a) Find the class width ($h$) for the frequency table. (1 Marks)
b) Calculate the median agricultural yield (2 Marks)
c) Find the number of farms having a yield of less than 60 quintals/acre. (1 Marks)
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4 Marks
Q15. Case Study: Speed Trap Monitoring on Highways
Traffic police monitored the speeds (in km/h) of 100 vehicles passing through an automated checkpoint: Speed (km/h) 40–50 50–60 60–70 70–80 80–90 90–100 Number of Vehicles 10 18 30 25 12 5
a) Determine the modal speed of vehicles at this checkpoint. (2 Marks)
b) State the lower limit of the modal class. (1 Marks)
c) Calculate the frequency of the median class if the cumulative frequency right before it is 28. (1 Marks)
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4 Marks
Q16. Case Study: Household Monthly Income Assessment
A local municipal ward assessed the monthly income (in thousands of ₹) of 75 families to allocate welfare support: Monthly Income (in ₹ thousands) 10–20 20–30 30–40 40–50 50–60 Number of Families 10 20 25 12 8
a) Find the empirical median income given that the mean is ₹33.2 thousand and mode is ₹34 thousand (2 Marks)
b) Determine the modal class for this distribution (1 Marks)
c) Find the class mark of the 4th class interval (40–50). (1 Marks)
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4 Marks
Q17. Case Study: Milk Packet Weight Quality Control
A dairy packaging unit checked the net volume (in ml) of 50 sealed milk packets chosen at random: Volume (in ml) 490–495 495–500 500–505 505–510 510–515 Number of Packets 5 15 20 7 3
a) Identify the modal class of the milk packets. (1 Marks)
b) Calculate the mean volume of milk per packet (2 Marks)
c) State the upper limit of the median class (1 Marks)
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4 Marks
Q18. Case Study: Daily Step Count Tracking of Office Employees
A fitness tracker company evaluated the daily step counts (in thousands) of 90 corporate employees over a work week: Step Count (in thousands) 2–4 4–6 6–8 8–10 10–12 Number of Employees 8 22 35 17 8
a) Find the median step count range (median class). (1 Marks)
b) Calculate the exact median step count value. (2 Marks)
c) What fraction of employees walk less than 6 thousand steps daily? (1 Marks)
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4 Marks
Q19. Case Study: Atmospheric Temperature Records
A meteorological department logged the maximum daily temperature (in °C) of a city during a 60-day summer window: Temperature (°C) 30–34 34–38 38–42 42–46 46–50 Number of Days 7 13 24 10 6
a) Find the modal temperature experienced in the city. (2 Marks)
b) State the lower limit of the median class. (1 Marks)
c) What is the cumulative frequency of the distribution up to the upper boundary of the modal class? (1 Marks)
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4 Marks
Q20. Case Study: Retail Store Daily Footfall Analysis
A shopping mall management recorded the hourly customer footfall across 50 peak hours during festival season sales: Customer Count 50–100 100–150 150–200 200–250 250–300 Frequency (Hours) 6 11 18 10 5
a) Determine the class interval that acts as the modal class. (1 Marks)
b) Calculate the average (mean) footfall per peak hour. (2 Marks)
c) Find the upper limit of the median class (1 Marks)
Academic Repository Disclaimer & எச்சரிக்கை அறிவிப்பு :
English: These model solutions are structured to global academic standards for self-assessment and practice purposes. Students are advised to verify with official textbooks for board examinations.
தமிழ்: இந்த மாதிரி கணிதத் தீர்வுகள் மாணவர்களின் சுய கற்றல் மற்றும் பயிற்சித் திறனுக்காக உலகளாவிய கல்வித் தரத்தில் உருவாக்கப்பட்டுள்ளன. தேர்வுகளுக்குத் தயாராகும் போது உங்கள் அதிகாரப்பூர்வ பாடப்புத்தகத்துடன் சரிபார்க்கவும்.
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