ROUTERA

Chapter 14 Statistics

Class 10th Maths Chapter Case Study Questions

Case Study 1: Analyzing Students' Heights

Case Description:
In a physical education class, the heights (in cm) of 10 students were measured and recorded as follows: 150, 155, 160, 162, 155, 158, 165, 170, 155, 160. The teacher aims to analyze the data to determine the average height of the students and identify any trends. To do this, they will calculate the mean, mode, and range of the heights.

MCQs:

  1. What is the mean height of the students?

    • A) 156.5 cm
    • B) 159 cm
    • C) 158 cm
    • D) 162 cm

  2. Which value appears most frequently in the data set?

    • A) 150 cm
    • B) 155 cm
    • C) 160 cm
    • D) 165 cm

  3. What is the range of the heights in the class?

    • A) 10 cm
    • B) 15 cm
    • C) 20 cm
    • D) 25 cm

  4. If one student measuring 165 cm is removed from the data, what will be the new mean height?

    • A) 157.5 cm
    • B) 158 cm
    • C) 159 cm
    • D) 160 cm

Case Study 2: Weekly Expenses of a Family

Case Description:
A family tracked their weekly expenses on groceries for four weeks as follows: ₹2000, ₹2200, ₹1800, ₹2100. The family wants to find the average weekly expense to budget better for the upcoming month. They will calculate the mean and create a frequency distribution to visualize their spending habits.

MCQs:

  1. What is the total expense over the four weeks?

    • A) ₹8000
    • B) ₹8200
    • C) ₹8600
    • D) ₹9000

  2. What is the mean weekly expense?

    • A) ₹2000
    • B) ₹2100
    • C) ₹2200
    • D) ₹2300

  3. Which of the following statements is true regarding the family’s spending?

    • A) They spent more in the first week.
    • B) Their spending increased every week.
    • C) The highest spending was ₹2200.
    • D) They spent less than ₹2000 in all weeks.

  4. If the family plans to reduce their expenses by 10% next month, what will be their new average weekly expense?

    • A) ₹1900
    • B) ₹2000
    • C) ₹2100
    • D) ₹2200

Case Study 3: Exam Scores of Students

Case Description:
The scores obtained by 15 students in a mathematics exam are as follows: 35, 40, 45, 50, 50, 55, 60, 65, 70, 75, 80, 80, 85, 90, 95. The teacher wants to determine the performance of the class by calculating the median score and identifying any outliers.

MCQs:

  1. What is the median score of the class?

    • A) 50
    • B) 60
    • C) 70
    • D) 75

  2. How many students scored above 80?

    • A) 5
    • B) 6
    • C) 7
    • D) 8

  3. Which score can be considered an outlier in this data set?

    • A) 35
    • B) 50
    • C) 70
    • D) 90

  4. If the highest score (95) is replaced with a score of 85, what will be the new median?

    • A) 60
    • B) 70
    • C) 75
    • D) 80

Case Study 4: Survey on Favorite Sports

Case Description:
A survey was conducted among 50 students about their favorite sports. The results are as follows: Cricket (15), Football (12), Basketball (10), Badminton (5), and Tennis (8). The sports teacher wants to create a pie chart to represent this data visually and analyze the preferences of the students.

MCQs:

  1. What percentage of students chose cricket as their favorite sport?

    • A) 25%
    • B) 30%
    • C) 35%
    • D) 40%

  2. Which sport is the least favorite among the students?

    • A) Cricket
    • B) Football
    • C) Basketball
    • D) Badminton

  3. If an additional 5 students are surveyed and all choose basketball, what will be the new total for basketball?

    • A) 10
    • B) 15
    • C) 20
    • D) 25

  4. In a pie chart representing these results, what would be the angle corresponding to the favorite sport of football?

    • A) 72°
    • B) 84°
    • C) 90°
    • D) 96°

Case Study 5: Monthly Temperatures

Case Description:
The monthly average temperatures (in °C) recorded for a city over six months are: January (15), February (17), March (20), April (22), May (25), June (28). The city council is interested in understanding the temperature trend and deciding when to schedule outdoor events. They will calculate the mean temperature and analyze the monthly changes.

MCQs:

  1. What is the mean temperature over the six months?

    • A) 18°C
    • B) 20°C
    • C) 21°C
    • D) 22°C

  2. Which month had the highest temperature?

    • A) January
    • B) March
    • C) May
    • D) June

  3. If July's average temperature is 30°C, how will it affect the mean temperature of the seven months?

    • A) It will decrease the mean.
    • B) It will increase the mean.
    • C) It will remain the same.
    • D) It cannot be determined.

  4. What is the increase in temperature from January to June?

    • A) 10°C
    • B) 12°C
    • C) 13°C
    • D) 14°C