#25 I\'m suppose to find the mean, modal class, variance, and standard deviation

Question

#25 I'm suppose to find the mean, modal class, variance, and standard deviation of the group of data. The answers are already included but I have tried several times to find the variance and the mean. I don't know what I'm doing wrong. I don't just want to write the answer, I need to solve this.

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c. Variance 11.6 h. Modal class 6-8 d. Standard deviation 3.4 Inches of Rain Shown here is a frequency distribution for the number of inches of rain received in 1 year in 25 selected cities in the United States. Number of inches 5. 30, Frequency 5.5-20.5 20.5-35.5 35.5-50.5 50.5-65.5 65.5-80.5 80.5-95.5 31. Find each of these. a. Mean 51.4 b. Modal class 35.5-50.5 C. Variance 451.5 d. Standard deviation 21.2

Explanation / Answer

Ans:

First of all,find out the mid point corresponding to each class.

e.g. for 5.5-20.5

mid point=(5.5+20.5)/2=13

a)Mean=1285/25=51.4

b)Modal class is which has highest frequency i.e. 8 and which corresponds to the class 35.5-50.5

c)Variance=10836/(25-1)=451.5

d)standard deviation=sqrt(451.5)=21.2

class midpoint(m) frequency(f) m*f (m-51.4)^2*f 5.5-20.5 13 2 26 2949.12 20.5-35.5 28 3 84 1642.68 35.5-50.5 43 8 344 564.48 50.5-65.5 58 6 348 261.36 65.5-80.5 73 3 219 1399.68 80.5-95.5 88 3 264 4018.68 Total= 25 1285 10836

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