Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
Daily sales figures for a week are shown in the bar chart given below (reconstructed to scale from the given data: Day 1–3000, Day 2–4000, Day 3–5000, Day 4–2000, Day 5–6000, Day 6–4000, Day 7–1000, all in Rs.). The mean daily sales and the standard deviation of the sample mean (integer value) are _____ and _____, respectively.
Figure (reconstructed to scale from given data):
Options:
(A) 3571, 1718
(B) 3715, 1915
(C) 3571, 1178
(D) 3715, 1591
Official Answer Key:
A
Step-by-Step Solution & Explanation
Mean = (3000+4000+5000+2000+6000+4000+1000)/7 = 25000/7 = 3571.43 ≈ 3571.
Sample standard deviation (using n−1 = 6 in the denominator, since this is a sample):
s = √[Σ(xᵢ−mean)²/(n−1)] = √[(571.43²+428.57²+1428.57²+1571.43²+2428.57²+428.57²+2571.43²)/6] ≈ 1718 (rounded to nearest integer). This matches option (A) exactly. Note this question asks for the standard deviation of the underlying data using the sample (n−1) formula, not the standard *error* of the mean (s/√n ≈ 649) — despite the wording ‘standard deviation of the sample mean’, the key’s value of 1718 corresponds to the sample standard deviation itself. Hence (A) is correct.
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.