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Giải bài 3.12 trang 67 sách bài tập toán 12 - Kết nối tri thức

Cho mẫu số liệu ghép nhóm về tuổi thọ của 20 thiết bị điện tử sau: Phương sai của mẫu số liệu ghép nhóm trên là A. 1,99. B. 2,99. C. 3,99. D. 4,99.

ꦗTổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Kết nối tri thức

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

Cho mẫu số liệu ghép nhóm về tuổi thọ của 20 thiết bị điện tử sau:

Phương sai của mẫu số liệu ghép nhóm trên là A. 1,99. B. 2,99. C. 3,99. D. 4,99.

Phương pháp giải - Xem chi tiết

Chọn giá trị đại diện cho mỗi nhóm số liệu sau đó áp dụng công thức để tìm phương sai.

Lời giải chi tiết

Đáp án: B.

Cỡ mẫu là \(n = 20\). Chọn giá trị đại diện cho mỗi nhóm số liệu, ta có bảng sau:

Tuổi thọ trung bình của các thiết bị điện tử là \(\overline x  = \frac{{3 \cdot 2 + 5 \cdot 8 + 7 \cdot 7 + 9 \cdot 3}}{{20}} = 6,1\) (năm). Phương sai của mẫu số liệu ghép nhóm trên là \(\frac{1}{{20}}\left( {{3^2} \cdot 2 + {5^2} \cdot 8 + {7^2} \cdot 7 + {9^2} \cdot 3} \right) - {6,1^2} = 2,99\). Vậy ta chọn đáp án B.

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