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Giải bài 5.35 trang 84 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Một học sinh dùng một dụng cụ đo đường kính d của một viên bi (đơn vị: cm) thu được kết quả sau:

Tổng hợp đề ไthi học kì 2 lớp 10 tất cả các môn - Kết nối tri thức

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Đề bài

Một học sinh dùng một dụng cụ đo đường kính d của một viên bi (đơn vị: cm) thu được kết quả sau:
Lần đo 1 2 3 4 5 6 7 8
d 6,50 6,51 6,50 6,52 6,49 6,50 6,78 6,49
a) Bạn Minh cho rằng kết quả đo ở lần 7 không chính xác. Hãy kiểm tra khẳng định này của Minh. b) Tính giá trị xấp xỉ cho đường kính của viên bi.

Phương pháp giải - Xem chi tiết

- Tính số trung bình của dãy dữ liệu trên \(\overline x  = \frac{{{x_1} + {x_2} + {x_3} + ... + {x_n}}}{n}\) - Tính trung vị của mẫu số liệu đã cho nếu số lẻ thì là số chính giữa còn nếu là số chẵn thì là trung bình cộng của hai số chính giữa - Trung vị \({Q_2}\), tìm nửa trung vị bên trái \({Q_2}\) và bên phải \({Q_2}\) (không bao gồm \(Q{}_2\) nếu n lẻ)Tìm khoảng tứ phân vị của dãy dữ liệu này \({\Delta _Q} = {Q_3} - {Q_1}\) -         Kiểm tra khẳng định của Minh bằng cách so sánh \({Q_3} + 1,5.{\Delta _Q}\) với 6,78

Lời giải chi tiết

a)      Số trung bình là:\(\overline x  = \frac{{6,50 + 6,51 + 6,50 + 6,52 + 6,49 + 6,50 + 6,78 + 6,49}}{8} = \frac{{52,29}}{8} = 6,53625\)Sắp xếp các dãy số liệu theo thứ tự tăng dần:
6,49 6,49 6,50 6,50 6,50 6,51 6,52 6,78
Ta có: \(n = 8\) nên trung vị là trung bình cộng của hai số chính giữa nên\({Q_2} = \frac{{6,50 + 6,50}}{2} = 6,5\)Trung vị dữ liệu bên phải \({Q_2}\) là:6,50     6,51    6,52     6,78Gồm 4 số do đó trung vị là trung bình cộng của hai số chính giữa nên\({Q_3} = \frac{{6,51 + 6,52}}{2} = 6,515\)Trung vị dữ liệu bên trái \({Q_2}\) là:6,49     6,49    6,50     6,50Gồm 4 số do đó trung vị là trung bình cộng của hai số chính giữa nên\({Q_1} = \frac{{6,49 + 6,50}}{2} = 6,495\)Khoảng tứ phân vị là: \({\Delta _Q} = 6,515 - 6,495 = 0,02\)Ta có: \({Q_3} + 1,5.{\Delta _Q} = 6,515 + 1,5.0,02 = 6,454 < 6,78\)\( \Rightarrow \) nghi ngờ của bạn Minh về lần đo thứ 9 không chính xác là đúng.b)     Giá trị lần đo thứ 9 là giá trị bất thường nên ta loại bỏ giá trị này và tính trung bình của 7 giá trị còn lại là:
\(\overline x  = \frac{{6,50 + 6,51 + 6,50 + 6,52 + 6,49 + 6,50 + 6,49}}{7} = \frac{{45,51}}{7} \approx 6,501\)

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