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Giải bài tập 2 trang 82 SGK Toán 12 tập 1 - Chân trời sáng tạo

Kết quả khảo sát thời gian sử dụng liên tục (đơn vị: giờ) từ lúc sạc đầy cho đến khi hết của pin một số máy vi tính cùng loại được mô tả bằng biểu đồ bên. a) Hãy cho biết có bao nhiêu máy vi tính có thời gian sử dụng pin từ 7,2 đến dưới 7,4 giờ? b) Hãy xác định số trung bình và độ lệch chuẩn của thời gian sử dụng pin.

🥀Tổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

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

Kết quả khảo sát thời gian sử dụng liên tục (đơn vị: giờ) từ lúc sạc đầy cho đến khi hết của pin một số máy vi tính cùng loại được mô tả bằng biểu đồ bên.
a) Hãy cho biết có bao nhiêu máy vi tính có thời gian sử dụng pin từ 7,2 đến dưới 7,4 giờ?
🃏b) Hãy xác định số trung bình và độ lệch chuẩn của thời gian sử dụng pin.

Phương pháp giải - Xem chi tiết

a) Quan sát đồ thị b) Tính giá trị đại diện Phương sai của mẫu số liệu ghép nhóm, kí hiệu \({S^2}\), được tính bởi công thức: \({S^2} = \frac{1}{n}[{n_1}{({c_1} - \overline x )^2} + {n_2}{({c_2} - \overline x )^2} + ... + {n_k}{({c_k} - \overline x )^2}]\) Trong đó: \(n = {n_1} + {n_2} + ... + {n_k}\) là cỡ mẫu \(\overline x  = \frac{1}{n}({n_1}{c_1} + {n_2}{c_2} + ... + {n_k}{c_k})\) là số trung bình Độ lệch chuẩn của mẫu số liệu ghép nhóm, kí hiệu \(S\), là căn bậc hai số học của phương sai.

Lời giải chi tiết

a) Có 2 máy vi tính có thời gian sử dụng pin từ 7,2 đến dưới 7,4 giờ

b)

Cỡ mẫu: n = 18 Số trung bình: \(\overline x  = \frac{{2.7,3 + 4.7,5 + 7.7,7 + 5.7,9}}{{18}} \approx 7,67\) Phương sai: \({S^2} = \frac{{2.7,{3^2} + 4.7,{5^2} + 7.7,{7^2} + 5.7,{9^2}}}{{18}} - 7,{67^2} \approx 0,04\) Độ lệch chuẩn: \(\sigma  = \sqrt {0,04}  \approx 0,19\)

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