Question

$<h6>Thirty women were examined in a hospital by a doctor and their of heart beats per minute were recorded and summarized as shown. Find the mean heart beats per minute for these women, choosing a suitable method$

Answer 1

Answer:

75.9

Step-by-step explanation:

Class Interval         (fi)                 (xi)               di = (xi - 75.5)           fidi

65 - 68                    2                    66.5               -9                           -18

68 - 71                     4                    69.5               -6                           -24

71 - 74                     3                     72.5               -3                           -9

74 - 77                    8                     75.5                0                            0

77 - 80                    7                     78.5                3                            21

80 - 83                   4                     81.5                 6                            24

83 - 86                   2                     84.5                9                            18

                             ----                                                                        -------

                           ∑fi = 30                                                                ∑fidi = 12

∴ d = ∑fidi/∑fi

             = 12/30

             = 0.4.

Mean(x) = d + a

             = 0.4 + 75.5

             = 75.9.

Hope it helps!

Answer 2

STEP DEVIATION METHOD:

Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number. If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h

Here, h is the class size of each class interval.

★★ Find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi.

★★ Class marks (xi) = ( lower limit + upper limit) /2

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn

MEAN = A + h ×(Σfiui /Σfi) , where ui = (xi - A )/h

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT

From the table : Σfiui = 4 , Σfi = 30

Let the assumed mean, A = 75.5, h = 3

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 75.5 + 3 (4/30)

= 75.5 + 4/10

= 75.5 + ⅖

= 75.5 + 0.4

Mean = 75.9

Hence, the mean heart beats per minute for women is 75.9 .

HOPE THIS ANSWER WILL HELP YOU….