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Giải bài 4 trang 132 sách bài tập toán 10 - Chân trời sáng tạo

Giá bán lúc 10h sáng của một mã cổ phiếu A trong 10 ngày liên tiếp được ghi lại ở biểu đồ sau (đơn vị: nghìn đồng).

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Đề bài

Giá bán lúc 10h sáng của một mã cổ phiếu A trong 10 ngày liên tiếp được ghi lại ở biểu đồ sau (đơn vị: nghìn đồng).

 

a) Viết mẫu số liệu thống kê giá của mã cổ phiếu A từ biểu đồ trên. b) Tìm khoảng biến thiện, khoảng tứ phân vị của mẫu số liệu đó. c) Tính trung bình, độ lệch chuẩn của mẫu số liệu trên.

Phương pháp giải - Xem chi tiết

Bước 1: Sắp xếp số liệu theo thứ tự không giảm: \({x_1},{x_2},...,{x_n}\) Khoảng biến thiên \(R = {x_n} - {x_1}\) Bước 2: Tìm trung vị \({Q_2}\) của mẫu số liệu  Bằng \({x_m}\) nếu \(n = 2m - 1\); là \(\frac{1}{2}({x_m} + {x_{m + 1}})\) nếu \(n = 2m\) Bước 3: Tìm tứ phân vị Tính \({Q_1}\)là trung vị của nửa số liệu đã sắp xếp bên trái \({Q_2}\) (không bao gồm trung vị nếu n lẻ) Tính \({Q_1}\)là trung vị của nửa số liệu đã sắp xếp bên phải \({Q_2}\) (không bao gồm trung vị nếu n lẻ) Khoảng tứ phân vị: \(\Delta Q = {Q_3} - {Q_1}\)  Tìm phương sai theo công thức \({S^2} = \frac{1}{n}\left( {{n_1}{x_1}^2 + {n_2}{x_2}^2 + ... + {n_k}{x_k}^2} \right) - {\overline x ^2}\) Độ lệch chuẩn \(S = \sqrt {{S^2}} \)

Lời giải chi tiết

a) Bảng thống kê
56,4 56,4 56,5 56,6

56,9

57,1

 57,4 57,7 57,7 57,8
b)+ Số cao nhất và thấp nhất lần lượt là 57,8 và 56,4 do đó khoảng biến thiên của dãy số liệu trên là: \(R = 57,8 - 56,4 = 1,4\)+ Tứ phân vị: \({Q_2} = \left( {56,9 + 57,1} \right) = 57\); \({Q_1} = 56,5;{Q_3} = 57,7\)c)+ Trung bình của mẫu số liệu là \(\overline x  = 57,05\)+ Phương sai: \({S^2} = 0,2916\)+ Độ lệch chuẩn: \(S = \sqrt {{S^2}}  = 0,54\)

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