Question

statics ch all formulas
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Answer 1

Answer:

Mean \bar{x}=\frac{\sum x}{n} x = Observations given n = Total number of observations

Standard Deviation S = \sigma = \sqrt{\frac{\sum (x-\bar{x})^{2}}{n}} x = Observations given \bar{x} = Mean n = Total number of observations

Answer 2

. Mean : The mean for grouped data can be found by :

(i) The direct method =X¯=∑fixi∑fiX¯=∑fixi∑fi

(ii) The assumed mean methodX¯=a+∑fidi∑fiX¯=a+∑fidi∑fi

Where di=xi−a.di=xi−a. a = Provisional mean

(iii) The step deviation method

X=a+∑fiui∑fi×h,whereUl=Xi−ahX=a+∑fiui∑fi×h,whereUl=Xi−ah

2. Mode : The mode for the grouped data can be found by using the formula :

mode=l+[f1−f02f1−f0−f2]×hmode=l+[f1−f02f1−f0−f2]×h

ll= lower limit of the modal class.

f1f1 = frequency of the modal class.

fofo = frequency of the preceding class of the modal class.

f2f2= frequency of the succeeding class of the modal class.

h = size of the class interval.

Modal class - class interval with highest frequency.

3. Median : Median of continuous series is:

(i) (N2)th(N2)th term (if number of terms are odd)

(ii) 12[(N2)thterm+(N2+1)thterm]12[(N2)thterm+(N2+1)thterm] (if number of terms are even]

(iii) The median for the grouped data can be found by using the formula :

median=l+[n/2−Cff]×hmedian=l+[n/2−Cff]×h

ll= lower limit of the median class.

n = number of observations.

Cf = cumulative frequency of class interval preceding the median class.

f = frequency of median class.

h = class size.

4.Empirical Formula : Mode = 3 median - 2 mean.

5.Cumulative frequency curve or an Ogive :

(i) Ogive is the graphical representation of the cumulative frequency distribution.

(ii) Less than type Ogive :

• Construct a cumulative frequency table.

• Mark the upper class limit on the x-axis.

(iii) More than type Ogive :

• Construct a frequency table.

• Mark the lower class limit on the x-axis.

(iv) To obtain the median of frequency distribution from the graph :

• Locate point of intersection of less than type Ogive and more than type Ogive :

Draw a perpendicular from this point on x-axis.

• The point at which it cuts the x-axis gives us the median.