Question

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. Find the mean heartbeats per minute for these women, choosing a suitable method. Number of heartbeats 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

Accepted Answer

To find the mean heartbeats per minute, we use the Direct Method by finding the class marks for each interval.

Step 1: Calculate the class mark ( $x_i$ ) for each class interval using the formula $x_i = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$ .

Step 2: Compute the product of frequency and class mark ( $f_i x_i$ ) for each class.

Calculation Table:

Class Interval	Number of women ( $f_i$ )	Class Mark ( $x_i$ )	$f_i x_i$
65 - 68	2	66.5	133.0
68 - 71	4	69.5	278.0
71 - 74	3	72.5	217.5
74 - 77	8	75.5	604.0
77 - 80	7	78.5	549.5
80 - 83	4	81.5	326.0
83 - 86	2	84.5	169.0
Total	$\sum f_i = 30$		$\sum f_i x_i = 2277$

Step 3: Apply the mean formula:

\text{Mean} = \frac{\sum f_i x_i}{\sum f_i}

\text{Mean} = \frac{2277}{30} = 75.9

The mean heartbeats per minute for these women is 75.9.

Explanation

Solution Steps

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