Thirty ladies were analyzed in a medical clinic by a specialist and the quantity of heart beats each moment were recorded and summed up as follows. Track down the mean heart beats each moment for these ladies, picking an appropriate strategy. 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
Thirty ladies were analyzed in a medical clinic by a specialist and the quantity of heart beats each moment were recorded and summed up as follows. Track down the mean heart beats each moment for these ladies, picking an appropriate strategy. 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:

From the given information, let us expect the mean as A = 75.5

    \[xi\text{ }=\text{ }\left( Upper\text{ }cutoff\text{ }+\text{ }Lower\text{ }limit \right)/2\]

Class size (h) = 3

Presently, find the ui and fiui as follows:

Class Interval      Number of ladies (fi)       Mid-point (xi)    

    \[ui\text{ }=\text{ }\left( xi\text{ }\text{ }75.5 \right)/h\]

fiui

65-68     2             66.5       -3           -6

68-71     4             69.5       -2           -8

71-74     3             72.5       -1           -3

74-77     8             75.5       0             0

77-80     7             78.5       1             7

80-83     4             81.5       3             8

83-86     2             84.5       3             6

Aggregate fi= 30                                             Sum fiui = 4

    \[Mean\text{ }=\text{ }x\text{ }=\text{ }A\text{ }+\text{ }h\sum fiui/\sum fi\]

= 75.5 + 3×(4/30)

= 75.5 + 4/10

= 75.5 + 0.4

= 75.9

Thusly, the mean heart beats each moment for these ladies is 75.9