Find mean variance and standard deviation for the following

Question

Problem 1: Find mean, variance and standard deviation of 1,3,4,5,6,6,10

Problem 2: Find mean, variance and standard deviation for the following frequency distribution table

X	5	15	25	35	45	55	65	75
F	3	7	9	23	15	8	6	4

Problem 3: Show that if x‾ is mean of the values x_i with weight f_i(i = 1, 2, 3....n), then ∑_i=1ⁿf_i(x_i - x‾) = 0.

Problem 4: Find median from the following data

Class	Frequency
10-25	7
25-40	20
40-55	40
55-70	26
70-85	5
85-100	2

Problem 5: Calculate the mode of the following distribution

Number of grains	100-110	110-130	130-140	140-160	160-170	170-180
Number of plants	11	40	27	34	12	6

Problem 6: Find mean deviation from the following data

30,40,70,20,60,50,10