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Giải bài tập 7.19 trang 53 SGK Toán 9 tập 2 - Kết nối tri thức

Giáo viên ghi lại thời gian chạy cự li 100 mét của các học sinh lớp 9A cho kết quả như sau: a) Nêu các nhóm số liệu và tần số tương ứng. b) Lập bảng tần số tương đối ghép nhóm.

Tổng hợp Đề thi vào 10 có đáp án và lời giải

Toán - Văn - Anh
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Đề bài

Giáo viên ghi lại thời gian chạy cự li 100 mét của các học sinh lớp 9A cho kết quả như sau:

a) Nêu các nhóm số liệu và tần số tương ứng. b) Lập bảng tần số tương đối ghép nhóm.

Video hướng dẫn giải

Phương pháp giải - Xem chi tiết

a) Cho bảng tần số:

Trong đó, tần số \({m_i}\) của nhóm \(\left[ {{a_i};{a_{i + 1}}} \right)\) là số giá trị của mẫu số liệu lớn hơn hoặc bằng \({a_i}\) và nhỏ hơn \({a_{i + 1}}\). b) + Tính tần số tương đối ứng với các giá trị trong mẫu dữ liệu: Nhóm \(\left[ {{a_i};{a_{i + 1}}} \right)\) có tần số \({m_i}\) thì có tần số tương đối là: \({f_i} = \frac{{{m_i}}}{n}.100\left( \%  \right)\) với m là tổng tất cả các tần số có trong mẫu số liệu. + Lập bảng tần số tương đối ghép nhóm:

Lời giải chi tiết

a) Các nhóm số liệu về thời gian \(\left[ {13;15} \right)\); \(\left[ {15;17} \right)\); \(\left[ {17;19} \right)\); \(\left[ {19;21} \right)\) có tần số tương ứng là 5; 20; 13; 2. b) Số học sinh tham gia chạy là: \(5 + 20 + 13 + 2 = 40\) (học sinh). Các nhóm số liệu về thời gian \(\left[ {13;15} \right)\); \(\left[ {15;17} \right)\); \(\left[ {17;19} \right)\); \(\left[ {19;21} \right)\) tương ứng có tần số tương đối là: \(\frac{5}{{40}} = 12,5\% ;\frac{{20}}{{40}} = 50\% ,\frac{{13}}{{40}} = 32,5\% ,\frac{2}{{40}} = 5\% \) Do đó, ta có bảng tần số tương đối ghép nhóm là:

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