Class 10 Maths
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Key Points - Statistics

- Mean: The arithmetic mean (or, simply mean) is the sum of the values of all the observations divided by the total number of observation.

- The mean for grouped data can be found by: 
 (i) The direct method = X = ∑ fixi / ∑ fi
 (ii) The assumed mean method X = a + ∑ fidi/ ∑ fi , Where  d i = x i − a.
 (iii) The step deviation method: X = a + ∑ fiui  / ∑ fi  × h, where U l = X i − a. / h
 
The mode for the grouped data can be found by using the formula:
mode = l +  [ (f1 − f 0)/(2f1 − f 0 − f 2)]  ×h

  = lower limit of the modal class.
 f1 = frequency of the modal class. fo = frequency of the preceding class of the modal class. f2 = frequency of the succeeding class of the modal class. h = size of the class interval.

Modal class - class interval with highest frequency.

- The median for the grouped data can be found by using the formula:
median = l + [(n/2 - CF)] × h
l = 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.

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

- 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.

(i) More than type Ogive:
(ii) Construct a frequency table.
(iii) Mark the lower class limit on the x-axis.

To obtain the median of frequency distribution from the graph:
(i) Locate point of intersection of less than type Ogive and more than type Ogive:
(ii) Draw a perpendicular from this point on x-axis.
(iii) The point at which it cuts the x-axis gives us the median.