A sample amount of profit for a certain company for the first 15 weeks of the year is given below: | Weeks | Amount of the Profit ($) | |-------|---------------------------| | 1 | 0 | | 2 | 70 | | 3 | 130 | | 4 | 130 | | 5 | 200 | | 6 | 230 | | 7 | 250 | | 8 | 270 | | 9 | 340 | | 10 | 410 | | 11 | 600 | | 12 | 660 | | 13 | 760 | | 14 | 770 | | 15 | 960 | What is the difference between the biased and unbiased estimators of the variance? | Financial Risk Manager Part 1 Quiz - LeetQuiz

Explanation:

Weeks	Amount of the Profit ($)	(Xᵢ − X̄)²
1	0	148481.778
2	70	99435.111
3	130	65195.111
4	130	65195.111
5	200	34348.444
6	230	24128.444
7	250	18315.111
8	270	13301.778
9	340	2055.111
10	410	608.444
11	600	46081.778
12	660	75441.778
13	760	140375.111
14	770	147968.444
15	960	330241.778
Mean	385.3333	1211173.333

Variance Calculations

Biased estimator
$\hat{\sigma}^2 = \frac{1}{15} \times 1211173.333 = 80744.89$
Unbiased estimator
$s^2 = \frac{15}{14} \times 80744.89 = 86512.38$
Difference
$86512.38 - 80744.89 = 5767.49$

A sample amount of profit for a certain company for the first 15 weeks of the year is given below:

Weeks Amount of the Profit ($)
1 0
2 70
3 130
4 130
5 200
6 230
7 250
8 270
9 340
10 410
11 600
12 660
13 760
14 770
15 960

What is the difference between the biased and unbiased estimators of the variance?

Exam-Like

Community

TTanishq

Last updated: April 18, 2026 at 07:00

0

A

5,867.50

17.6%

B

5,503.90

11.8%

C

5,767.49

35.3%

D

5,867.87

35.3%

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