Question

During a medical checkup, the number of heartbeats per minute of 40 patients were recorded and summarised as follows:

Number of heartbeats per minute	64 − 68	68 − 72	72 − 76	76 − 80	80 − 84	84 – 88
Number of patients	6	8	10	12	3	1

Find the mean heartbeats per minute for these patients.

Answer 1

Here, h = 4

Let the assumed mean, A be 78.

Number of Heartbeats per Minute	Mid-Values(xi)	Number of Patients (fi)	${\mathit{d}}_i\mathbf{=}{\mathit{x}}_{\mathit{i}}\mathbf{-}\mathbf{78}$	${\mathit{u}}_i\mathbf{=}\frac{{\mathit{x}}_i\mathbf{-}\mathbf{78}}{\mathbf{4}}$	${\mathit{f}}_{\mathit{i}}{\mathit{u}}_{\mathit{i}}$
64−68	66	6	−12	−3	−18
68−72	70	8	−8	−2	−16
72−76	74	10	−4	−1	−10
76−80	78	12	0	0	0
80−84	82	3	4	1	3
84−88	86	1	8	2	2
		$\underset{}{\sum f_i=40}$			$\underset{}{\sum f_i{u}_i=-39}$

We know

Mean $=A+h\times \left(\frac{\sum _{}{f}_i{u}_i}{\sum _{}{f}_i}\right)$

∴ Mean heartbeats per minute for these patients

$$\begin{gathered} =78+4\times \left(\frac{-39}{40}\right) \\ =78-3.9 \\ =74.1 \end{gathered}$$

Thus, the mean heartbeats per minute for these patients is 74.1.