The empirical relationship between the three measures of central tendency is:
Correct Answer:(A) 3 Median = Mode + 2 Mean
Step-by-step Solution:
Standard empirical formula: 3 Median = Mode + 2 Mean.
Q2MCQ1 Mark
Mode of a grouped frequency distribution is given by:
Correct Answer:(A) l + [(f₁ - f₀)/(2f₁ - f₀ - f₂)] × h
Step-by-step Solution:
Formula for mode of grouped data.
Q3MCQ1 Mark
Class mark of class interval 10 - 25 is:
Correct Answer:(A) 17.5
Step-by-step Solution:
Class mark = (10 + 25)/2 = 35/2 = 17.5.
Q4MCQ1 Mark
If mean of observations x, x+3, x+5, x+7, x+10 is 9, then mean of last 3 observations is:
Correct Answer:(A) 11.33
Step-by-step Solution:
Sum = 5x + 25 = 45 ⇒ x = 4. Last 3 obs: 9, 11, 14. Mean = 34/3 = 11.33.
Q5Assertion-Reason1 Mark
Assertion (A): Mode of a frequency distribution can be determined graphically using a Histogram.
Reason (R): The peak rectangle in a histogram corresponds to the modal class.
Correct Answer:(A) Both (A) and (R) are true and (R) is the correct explanation of (A).
Step-by-step Solution:
Both A and R are true and R explains A.
Q6Assertion-Reason1 Mark
Assertion (A): Mean of grouped data can be calculated using Direct Method, Assumed Mean Method or Step Deviation Method.
Reason (R): All three methods give the exact same value of mean.
Correct Answer:(A) Both (A) and (R) are true and (R) is the correct explanation of (A).
Step-by-step Solution:
Both A and R are true.
Q7Short Answer2 Marks
Find the mean of first 10 natural numbers.
Correct Answer:5.5
Step-by-step Solution:
Sum = 10(11)/2 = 55. Mean = 55 / 10 = 5.5.
Q8Short Answer2 Marks
If mean = 27 and median = 33, find mode using empirical formula.
If mean of distribution is 50 and sum of frequencies is 120, find missing frequencies f₁ and f₂ for classes (0-20:17, 20-40:f₁, 40-60:32, 60-80:f₂, 80-100:19).
Case Study Scenario: A literacy survey of 35 cities gave data: Literacy rate % (45-55: 3, 55-65: 10, 65-75: 11, 75-85: 8, 85-95: 3).
Question: Find mean literacy rate.
Correct Answer:69.43 %
Step-by-step Solution:
Direct method: Σf = 35, Σfx = 2430. Mean = 2430 / 35 = 69.43 %.
Q17Case Study4 Marks
Case Study Scenario: Life of 400 neon lamps data: Hours (1500-2000: 14, 2000-2500: 56, 2500-3000: 60, 3000-3500: 86, 3500-4000: 74, 4000-4500: 62, 4500-5000: 48).
Question: Find median life time of a lamp.
Correct Answer:3406.98 hours
Step-by-step Solution:
N/2 = 200. Median class 3000-3500. l=3000, cf=130, f=86, h=500. Median = 3000 + [(200-130)/86]×500 = 3406.98 hours.
Q18PYQ5 Marks
Median of following data is 525. Find x and y if total frequency is 100: (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).
Correct Answer:x = 9, y = 15
Step-by-step Solution:
x + y = 24. Median 525 lies in 500-600. 525 = 500 + [(50-36-x)/20]×100 ⇒ 25 = (14-x)5 ⇒ 14-x = 5 ⇒ x = 9, y = 15.
Q19PYQ5 Marks
Mean of following distribution is 18. Find missing frequency f: (11-13:7, 13-15:6, 15-17:9, 17-19:13, 19-21:f, 21-23:5, 23-25:4).
