Question

Several years ago, the state of California launched an aggressive advertisement campaign against smoking. We're interested in the usefulness of this campaign among college students. We've interviewed students from 24 college campuses in California and recorded for each campus the percentage of students who claimed that they had encountered at least one anti-smoking advertisement on campus in the past month. Our results are displayed in the following histogram: Frequency 15 12 10 48 64 80 32 Percentage of students 16 Based on this histogram, estimate the standard deviation of the sample of 24 percentages. Carry your intermediate computations to at least four decimal places, and round your answer to at least one decimal place.

Answer 1

Solution:- midpoint : 24,40,56,72

frequency : 2,12,6,4

Step by Step Calculation:

Σ (M . F)

µ = ---------------------   

ΣF

Total = 24 x 2 + 40 x 12 + 56 x 6 + 72 x 4 = 1152

ΣF = 24

Mean = 1152/24

Mean = 48

σ2 = (ΣF . M2 - n * µ2)/(n-1)

ΣF . M2 = 2 x 242 + 12 x 402 + 6 x 562 + 4 x 722

= 59904

σ2 = (59904 - 24 x 482)/ 23

σ2 = 200.3478

σ = 14.1544