Question

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

"Number of heart beats
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

Answer 1

To calculate the mean heart beats per minute, find the mid-point for each class interval, multiply by the frequency, sum the products, and divide by the total number of women.

Step-by-step explanation:

To calculate the mean heart beats per minute for the thirty women examined, we can use the grouped data method. Since we have the ranges of heart beats per minute and the number of women in each range, we perform the following steps:

• Find the mid-point of each class interval by taking the average of the lower and upper boundaries of each interval.
• Multiply the mid-point by the frequency (the number of women) in that class.
• Add up all the products from step 2 to get the sum of all heart beats.
• Sum the frequencies (total number of women) to get the total frequency.
• Divide the sum of all heart beats by the total frequency to find the mean heart rate.

Calculation Steps:

1. Class intervals: [65–68, 68–71, 71–74, 74–77, 77–80, 80–83, 83–86]
2. Mid-points: [(65+68)/2, (68+71)/2, (71+74)/2, (74+77)/2, (77+80)/2, (80+83)/2, (83+86)/2] = [66.5, 69.5, 72.5, 75.5, 78.5, 81.5, 84.5]
3. Multiply each mid-point by its frequency and sum up: (66.5*2)+(69.5*4)+(72.5*3)+(75.5*8)+(78.5*7)+(81.5*4)+(84.5*2)
4. Add up the frequencies: 2+4+3+8+7+4+2 = 30 women
5. Calculate the mean heart rate: Sum of all heart beats / 30

The resulting mean heart rate will provide a measure of the average heart rate for the group of women examined.