Question

13.
The time taken by 50 students to complete a 100 meter race are given below. Find its
standard deviation.
Time taken(sec) 8.5-9.5 9.5-10.5 10.5-11.5 11.5-12.5 12.5-13.5
Number of students 6
8 17 10 9​

Answer 1

Given:

Time taken(sec): 8.5-9.5,  9.5-10.5,  10.5-11.5,  11.5-12.5,  12.5-13.5

No. of students:       6               8                17              10                9​

To find: standard deviation (σ).

Solution:

standard deviation (σ) = c × √∑$(f_id_i^2)/N$ - ∑$(f_id_i)/N$

                                       = 1 × √(144/50) - (58/50)

                                        = √86/50

                                        = 1.311

answer: standard deviation (σ) is 1.311

Answer 2

Solution :-

Time(sec.) fi xi fixi fixi²

8.5 - 9.5 6 9 54 486

9.5 - 10.5 8 10 80 800

10.5 - 11.5 17 11 187 2057

11.5 - 12.5 10 12 120 1440

12.5 - 13.5 9 13 117 1521

∑f = 50 ∑fixi = 558 ∑fixi² = 6304

then,

→ Variance = 1/(N - 1) [∑fixi² - 1/N(∑fixi)²]

→ Variance = 1/(50 - 1) [6304 - (1/50)(558)²]

→ Variance = (1/49)[6304 - 6227.28]

→ Variance = (1/49)(76.72) = 1.565

Therefore,

→ Standard deviation = √(variance) = √(1.565) = 1.25 (Ans.)

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