Answer to Question #138153 in Statistics and Probability for Ally

Question

The Bureau of Food and Drugs (BFD) monitors the effectiveness of new drugs. Some medications cause serious side effects. One particular antihistamine drug can lead to drowsiness or adversely affect the user’s ability to operate a motor vehicle. The following is a list of the frequency of reaction and the age of the person using the medication. Find the mean, median and mode. Age of Person No. Who Experienced a Reaction 16-25 12 26-35 18 36-45 22 46-55 19 56-65 17 66-75 8 76-85 4

Answer 1

Solution

Mean

$$Mean, \bar{x} ={\sum fx \over \sum f}$$ $$={4560 \over 100}=45.6$$

Ans: 45.6

Median

$$Median = L+ {h \over f}({N \over 2}-cf)$$

where; L= lower limit of the median class, h=class width of median class, f=frequency of median class, N=total frequency, cf= cum. frequency above median class.

${100 \over 2}=50$ , hence the age of the 50th person is the median. median class is between 36-45

$$\therefore Median = 35.5 + {10 \over 22}({100 \over 2}-30)=44.590$$

Ans: 44.590

Mode

$$Mode = L+({f_1-f_0 \over 2f_1 -f_0 - f_2})i$$

where; L = lower limit of modal class

f₁= frequency of the modal group,

f₀=frequency of the group before modal group

f₂= frequency of group after the modal group

i= class width of modal group

36-45 is the modal group since it has the highest frequency.

$$Mode= 35.5+({22-18 \over 2(22)-18-19})10=41.2143$$

Ans: 41.2143