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Giải bài 5.9 trang 77 sách bài tập toán 10 - Kết nối tri thức với cuộc sống

Tổng số ca mắc Covid-19 tính đến ngày 26-8-2021 tại Thành phố Hồ Chí Minh và một số tỉnh lân cận được thống kê như sau:

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

Toán - Văn - Anh - Lí - Hóa - Sinh - Sử - Địa...
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Đề bài

Tổng số ca mắc Covid-19 tính đến ngày 26-8-2021 tại Thành phố Hồ Chí Minh và một số tỉnh lân cận được thống kê như sau:
190 174 81 182 19 728 19 048 8 155 6 103 5 807  
4 544 3 760 3 297 2 541 2 000 1 934 1 602 1 195

(Theo Bộ Y Tế)

a) Tính số trung bình và trung vị cho dãy số liệu trên. b) Giải thích tại sao số trung bình và trung vị lại khác nhau nhiều?

Phương pháp giải - Xem chi tiết

-  Áp dụng công thức tính số trung bình \(\overline x  = \frac{{{x_1} + {x_2} + ... + {x_n}}}{n}\) -  Sắp xếp các giá trị theo thứ tự tăng dần => tìm vị trí chính giữa -  So sánh số trung bình với trung vị và đưa ra kết luận

Lời giải chi tiết

a) Ta có: \(n = 15\)Số trung bình cộng số ca mắc Covid-19 của Thành phố Hồ Chí Minh và một số tỉnh lần cận là:\(\overline x  = \frac{{190174 + 81182 + 19728 + ... + 1934 + 1602 + 1195}}{{15}} = \frac{{351070}}{{15}} \approx 23404,667\)Sắp xếp dãy số liệu theo thứ tự tăng dần:
1 195 1 602 1 934 2 000 2 541 3 297 3 760  
4 544 5807 6 103 8 155 19 048 19 728 81 182 190 174
Vì \(n = 15\) nên vị trí chính giữa là vị trí số 8. Do đó, trung vị là 4 544.b) Số trung bình lớn hơn rất nhiều số trung vị là do trong dãy số có một giá trị rất lớn là 190 174. Trung vị không bị ảnh hưởng bởi giá trị bất thường này.

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