Question 4 Find the mean and variance for the data
xi 6 10 14 18 24 28 30
f i 2 4 7 12 8 4 3
Class X1 - Maths -Statistics Page 371
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see attachment ,
we get,
so,
![Mean(\overline{x})=\frac{\sum{f_ix_i}}{\sum{f_i}}\\\\=\frac{760}{40}=19\\\\\\NOW, variance=\frac{\sum{f_ix_i^2}}{\sum{f_i}}-[\frac{\sum{f_ix_i}}{\sum{f_i}}]^2\\\\=\frac{16176}{40}-[\frac{760}{40}]^2\\\\=404.4-(19)^2\\\\=404.4-361=43.4](https://tex.z-dn.net/?f=Mean%28%5Coverline%7Bx%7D%29%3D%5Cfrac%7B%5Csum%7Bf_ix_i%7D%7D%7B%5Csum%7Bf_i%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B760%7D%7B40%7D%3D19%5C%5C%5C%5C%5C%5CNOW%2C+variance%3D%5Cfrac%7B%5Csum%7Bf_ix_i%5E2%7D%7D%7B%5Csum%7Bf_i%7D%7D-%5B%5Cfrac%7B%5Csum%7Bf_ix_i%7D%7D%7B%5Csum%7Bf_i%7D%7D%5D%5E2%5C%5C%5C%5C%3D%5Cfrac%7B16176%7D%7B40%7D-%5B%5Cfrac%7B760%7D%7B40%7D%5D%5E2%5C%5C%5C%5C%3D404.4-%2819%29%5E2%5C%5C%5C%5C%3D404.4-361%3D43.4 "Mean(\overline{x})=\frac{\sum{f_ix_i}}{\sum{f_i}}\\\\=\frac{760}{40}=19\\\\\\NOW, variance=\frac{\sum{f_ix_i^2}}{\sum{f_i}}-[\frac{\sum{f_ix_i}}{\sum{f_i}}]^2\\\\=\frac{16176}{40}-[\frac{760}{40}]^2\\\\=404.4-(19)^2\\\\=404.4-361=43.4")
hence, answer is 43.4
we get,
so,
hence, answer is 43.4
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