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

The class mark (x_i) is calculated using the formula:

Class Mark (x_i) = `("Lower Limit" + "Upper Limit")/2`

Number of Heartbeats per Minute (Class Interval)	Number of Patients (fi)	Class Mark (xi)	Product (fixi)
64 – 68	6	66	6 × 66 = 396
68 – 72	8	70	8 × 70 = 560
72 – 76	10	74	10 × 74 = 740
76 – 80	12	78	12 × 78 = 936
80 – 84	3	82	3 × 82 = 246
84 – 88	1	86	1 × 86 = 86
Total	Σfi = 40		Σfixi = 2964

Using the formula for the mean of grouped data:

Mean `(barx) = (sumf_ix_i)/(sumf_i)`

Substitute the values from the table:

`barx = 2964/40 = 74.1`

The mean heartbeats per minute for these patients is 74.1 bpm.