Test Index

NCERT Class XI Mathematics - Statistics - Solutions

© examsnet.com
Question : 19 of 34
Marks: +1, -0
Find the mean and variance for the following frequency distributions in Exercises 7 and 8.
Classes Frequencies
0 - 302
30 - 60 3
60 - 905
90 - 12010
120 - 150 3
150 - 180 5
180 - 210 2
Solution:  
ClassesMid values
xix_i		 fif_i uiu_i = xi−10530\frac{x_i-105}{30} fiuif_iu_i fiui2f_iu_i^2
0 - 30 15 2 - 3- 6 18
30 - 6045 3 - 2- 6 12
60 - 90 75 5 - 1- 5 5
90 - 120 10510 0 0 0
120 - 150 13531 33
150 - 180 165 52 10 20
180 - 210 95 2 3 618
30 2 76
Let assumed mean (A) = 105
Mean (x−)\left(\overset{-}{x}\right) = A + ΣfiuiN\frac{\Sigma f_iu_i}{N} × h = 105 + 230\frac{2}{30} × 30 = 107
Variance (σ2)(\sigma^2) = h2N2[NΣfiui2−(Σfiui)2]\frac{h^2}{N^2} \left[N\Sigma f_iu_i^2 - (\Sigma f_iu_i)^2\right] = 900900\frac{900}{900} [30 × 76 - 4]
= [2280 - 4] = 2276
© examsnet.com
Go to Question:
Prev Question
Next Question