# Problems With Statistics

Introduction to problems with statistics:

The word ‘Statistics’ has been taken from  Italian word ‘Statista’ or Latin word ‘Status’ or French word ‘Statistique’or German word ‘Statistik’ each of which means apolitical state. Statistics problems are aggregates that are made up of number of individual or cases. A single sale or accident or observations will not constitute a statistics. Statistics problems are related to other facts and should be homogeneous and comparable.

## Concepts related with Statistics problems:

Dispersion: The collection of data is represented in different forms. From the data we have learnt to calculate the measures of the central tendency likes mean,median and mode.

Range: Range is the method for measuring  dispersion. It defined as  difference between the larger(L)and the smaller(S) values in the series. Range = L – S, L = largest value, S = smallest value

Formulas to be used to sovle problems with statistics

Coefficient of range = `(L-S)/(L+s)`

Standard Deviation: Standard Deviation  defined as  positive square root of  mean of the squared deviations of the data . It is denoted by σ .

n                                                                       n

σ =√ ∑ (xi-x)2    (or)     σ =   √ ∑ di2/n        where di2 = (xi-x)

I=1        n                                 I=1

Example problems with statistics:

Pro 1: Find the range of the data 27,28,34,36,39,59. Also find the coefficient of range.

Solution : Largest value L = 59; Smallest value S = 27

Range = L – S = 59–27 = 32

Coefficient of Range =  `(L-S)/(L+s) = (59 -27)/(59+27) = 32/86`    =0.372

Pro 2:  The marks obtained by 10 students in a class test out statistics of 100 marks are 62, 49, 71,75, 33, 41, 100, 88, 50, 31. Calculate the statistics standard deviation of the marks.

Solution:x  = `(sum x)/ n = (62+49+71+75+33+41+100+88+50+31)/10` = 60

σ =√Σd2/n

=√4886/10

=  √488.6

=22.10

Thus we can see how the problems with statistics are sovled easily by using the formulas.

## Practice problems with statistics:

Pro 1: The weights of seven persons in kg are 46, 49.5, 52.5, 38, 45, 79.5, 84.5. Find  the range and the coefficient of range.

solution:Range =0.379

Pro 2:The largest value of a data is 98. If the range of the data is 73, find the smallest value of the data.

solution: The smallest value = 25.

Pro 3:Calculate the standard deviation for the data 14, 22, 9, 15, 20, 17, 12, 11

solution: standard deviation=4.18

Pro 4: The following are the bowling rate per over of a player in 12 cricket matches : 6.5, 5.0, 5.2, 5.3, 5.5, 5.0, 4.7, 4.5, 6.3, 3.0, 4.0, 9.0. Find the standard deviation.

solution: standard deviation:1.42