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Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows - CBSE Class 10 - Mathematics

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Question

Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows. Fine the mean heart beats per minute for these women, choosing a suitable method.

 

Number of heart beats per minute 65 − 68 68­ − 71 71 −74 74 − 77 77 − 80 80 − 83 83 − 86
Number of women 2 4 3 8 7 4 2

Solution

To find the class mark of each interval (xi), the following relation is used

`x_i  = ("Upper class limit + Lower class limit")/2`

Class size, h, of this data = 3

Taking 75.5 as assumed mean (a), di, ui, fiui are calculated as follows.

Number of heart beats per minute

Number of women

fi

xi di = x− 75.5 ui = di/3 fiui
65 − 68 2 66.5 − 9 -3 -6
68 − 71 4 69.5 − 6 -2 -8
71 − 74 3 72.5 − 3 -1 -3
74 − 77 8 75.5 0 0 0
77 − 80 7 78.5 3 1 7
80 − 83 4 81.5 6 2 8
83 − 86 2 84.5 9 3 6
Total 30       4

From the table, we obtain

`sumf_i = 30`

`sumf_iu_i = 4`

mean `barx=a+((sumf_iu_i)/(sumf_i))xxh`

`= 75.5 +(4/30) xx 3`

= 75.5 + 0.4 = 75.9

Therefore, mean hear beats per minute for these women are 75.9 beats per minute.

  Is there an error in this question or solution?

APPEARS IN

 NCERT Solution for Mathematics Textbook for Class 10 (2019 to Current)
Chapter 14: Statistics
Ex. 14.10 | Q: 4 | Page no. 271
Solution Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows Concept: Mean of Grouped Data.
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