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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. Fine the mean heart beats per minute for these women, choosing a suitable method.Number of heart beats per minute68­−7171−7474−7777−8080−8383−86Number of Women2438742

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Solution

## Given data is,Number of heart beats per minute68­−7171−7474−7777−8080−8383−86Number of Women2438742To find the class mark of each interval (xi), the following relation is used.xi=Upper class limit+Lower class limit2Class size, h of this data =3Taking 75.5 as assumed mean (a), di and ui are calculated as follows.Number of heart beats per minuteNumber of Womenxidi=xi−aui=di3fiui65−68266.5−9−3−668−71469.5−6−2−671−74372.5−3−1−674−77875.500−677−80778.531−680−83481.562−683−86284.593−6Total∑fi=30∑fiui=4From the table,∑fi=30∑fiui=4size of the class interval h=3.Mean =a+(∑fiui∑fi)h=75.5+(430)×3=75.5+410=75.5+0.4=75.9Therefore, mean hear beats per minute for these women are 75.9 beats per minute.

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