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Bài 5.11 trang 145 SGK Toán 11 tập 1 - Cùng khám phá

Hãy xác định mốt của mẫu số liệu cho bởi bảng tần số ghép nhóm dưới đây:
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Đề bài

♊Hãy xác định mốt của mẫu số liệu cho bởi bảng tần số ghép nhóm dưới đây:

 

Phương pháp giải - Xem chi tiết

Nhóm chứa mốt là nhóm mà có tần số nhiều nhất Mốt của mẫu số liệu ghép nhóm được tính theo công thức: \({M_0} = {L_m} + \frac{a}{{a + b}}.h\) Trong đó: \({L_m}\) là đầu mút trái của nhóm chứa mốt; \(h\) là độ dài của nhóm chứa mốt; \(a = {n_0} - {n_1};b = {n_0} - {n_2}\) với \({n_0};{n_1};{n_2}\) tương ứng là tần số của nhóm chứa mốt, nhóm liền kề trước và nhóm liền kề sau nhóm chứa mốt.

Lời giải chi tiết

Nhóm chứa mốt là \(\left[ {8;10} \right)\) với tần số là 18. Khi đó, \({L_m} = 8;h = 10 - 8 = 2\)\(a = 18 - 8 = 10;b = 18 - 11 = 7\)Ta có \({M_0} = {L_m} + \frac{a}{{a + b}}.h = 8 + \frac{{10}}{{10 + 7}}.2 \approx 9,2\)

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