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Giải bài tập 13 trang 91 SGK Toán 12 tập 2 - Kết nối tri thức

Thống kê thời gian trong tuần dành cho đọc sách của một số nhân viên trong một công ty được cho trong bảng sau: a) Khoảng biến thiên của mẫu số liệu ghép nhóm này là A. 13. B. 10. C. 8. D. 6. b) Độ lệch chuẩn của mẫu số liệu ghép nhóm này là (làm tròn kết quả đến hàng phần trăm) A. 1,99. B. 2,02. C. 3,97. D. 4,09.

✨Tổng 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

 
 
Thống kê thời gian trong tuần dành cho đọc sách của một số nhân viên trong một công ty được cho trong bảng sau:

a) Khoảng biến thiên của mẫu số liệu ghép nhóm này là A. 13. B. 10. C. 8. D. 6. b) Độ lệch chuẩn của mẫu số liệu ghép nhóm này là (làm tròn kết quả đến hàng phần trăm) A. 1,99. B. 2,02. C. 3,97. D. 4,09.
 

Phương pháp giải - Xem chi tiết

a) Sử dụng kiến thức về khoảng biến thiên của mẫu số liệu ghép nhóm để tính: Cho mẫu số liệu ghép nhóm:

Khoảng biến thiên của mẫu số liệu ghép nhóm trên là: \(R = {a_{k + 1}} - {a_1}\). b) Sử dụng kiến thức về phương sai của mẫu số liệu ghép nhóm để tính: Phương sai của mẫu số liệu ghép nhóm, kí hiệu là \({s^2}\), là một số được tính theo công thức sau: \({s^2} = \frac{1}{n}\left( {{m_1}x_1^2 + ... + {m_k}x_k^2} \right) - {\left( {\overline x } \right)^2}\), trong đó \(n = {m_1} + ... + {m_k}\) với \(\overline x  = \frac{{{m_1}{x_1} + ... + {m_k}{x_k}}}{n}\) là số trung bình của mẫu số liệu ghép nhóm. Sử dụng kiến thức độ lệch chuẩn của mẫu số liệu ghép nhóm để tính: Độ lệch chuẩn của mẫu số liệu ghép nhóm, kí hiệu là s, là căn bậc hai số học của phương sai của mẫu số liệu ghép nhóm, tức là \(s = \sqrt {{s^2}} \)
 

Lời giải chi tiết

a) Khoảng biến thiên của mẫu số liệu là: \(R = 10 - 0 = 10\) Chọn B b) Mẫu số liệu ghép nhóm với giá trị đại diện:

Số giờ đọc trung bình: \(\overline x  = \frac{{1.3 + 3.8 + 5.15 + 7.7 + 9.2}}{{3 + 8 + 15 + 7 + 2}} = \frac{{169}}{{35}}\) (giờ) Phương sai: \({s^2} = \frac{1}{{35}}\left( {{1^2}.3 + {3^2}.8 + {5^2}.15 + {7^2}.7 + {9^2}.2} \right) - {\left( {\frac{{169}}{{35}}} \right)^2} = \frac{{4864}}{{1225}}\) Độ lệch chuẩn: \(s = \sqrt {\frac{{4864}}{{1225}}}  \approx 1,99\) Chọn A
 

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