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Giải bài tập 3 trang 92 SGK Toán 12 tập 1 - Cánh diều

Bảng 21 biểu diễn mẫu số liệu ghép nhóm về độ tuổi của cư dân trong một khu phố. Tính phương sai và độ lệch chuẩn của mẫu số liệu đó.

ꦕTổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Cánh diều

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

 
 
Bảng 21 biểu diễn mẫu số liệu ghép nhóm về độ tuổi của cư dân trong một khu phố. Tính phương sai và độ lệch chuẩn của mẫu số liệu đó.

 

Phương pháp giải - Xem chi tiết

\({s^2} = \frac{{{n_1}.{{({x_1} - \overline x )}^2} + {n_2}{{({x_2} - \overline x )}^2} + ... + {n_p}{{({x_p} - \overline x )}^2}}}{n}\) \(s = \sqrt {{s^2}} \)
 

Lời giải chi tiết

Số trung bình cộng của mẫu số liệu ghép nhóm là: \(\overline x  = \frac{{25.25 + 20.35 + 20.45 + 15.55 + 14.65 + 6.75}}{{100}} = 44,1\) Phương sai của mẫu số liệu ghép nhóm là:

\({s^2} = \frac{{25.{{(25 - 44,1)}^2} + 20.{{(35 - 44,1)}^2} + 20.{{(45 - 44,1)}^2} + 15.{{(55 - 44,1)}^2} + 14.{{(65 - 44,1)}^2} + 6.{{(75 - 44,1)}^2}}}{{100}} = 244,19\)

Độ lệch chuẩn của mẫu số liệu ghép nhóm là: \(s = \sqrt {{s^2}}  = \sqrt {244,19}  \approx 15,63\)
 

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