Mean of the Tabulated Data

In the mean of the tabulated data, if the frequencies of n observations

x₁, x₂, x₃, ………. x_n are f₁, f₂, f₃ ………. f_n, then

Mean of the tabulated data
= (f₁x₁ + f₂x₂ + f₃x₃ ……… f_nx_n)/( f₁ + f₂ + f₃ ………. f_n) = (∑ f_ix_i)/(∑f_i)

Worked-out examples on mean of the tabulated data:

1. Find the mean weight of 50 girls from the following table.

Weight in kg	40	42	34	36	46
No. of girls	6	6	15	14	7

Solution:

Mean = (f₁x₁ + f₂x₂ + f₃x₃ + f₄x₄ + f₅x₅)/(f₁ + f₂ + f₃ + f₄ + f₅)

     = (40 × 6 + 42 × 6 + 34 × 15 + 36 × 14 + 46 × 7)/(8 + 6 + 15 + 14 + 7)

     = (240 + 252 + 510 + 504 + 322)/50

     = 1828/50

     = 36.56

2. If the mean of the following frequency distributions is 9, find the value of `a’. Write the tally marks also.

Variable (xi)	4	6	8	10	12	15
Frequency (fi)	8	9	17	a	8	4

Solution:

Frequency distribution table

Mean = (∑f_ix_i)/(∑f_i)

But given mean = 9

So, we have (378 + 10a)/(46 + a) = 9

378 + 10a = 9(46 + a)

378 + 10a = 414 + 9a

10a - 9a = 414 - 378

a = 36

`

● Statistics

• Real Life Statistics
  
• Terms Related to Statistics
  
• Frequency Distribution of Ungrouped and Grouped Data
  
• Use of Tally Marks
  
• Class Limits in Exclusive and Inclusive Form
  
• Construction of Bar Graphs
  
• Mean
  
• Mean of the Tabulated Data
  
• Mode
  
• Median
  
• Construction of Pie Chart
  
• How to Construct a Line Graph?
  

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