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

Solution:

We will use the step-deviation method to solve this question because the data given is large and will be convenient to apply if all the dᵢ have a common factor.

When the numerical values of xᵢ and fᵢ are large, finding the product of xᵢ and fᵢ becomes tedious. We can change each xᵢ to a smaller number so that our calculations become easy. Now we have to subtract a fixed number from each of these xᵢ.

• The first step is to select one among the xᵢ as the assumed mean which is named as ‘a’. Also, to further reduce our calculation work, we may take ‘a’ to be that xᵢ which lies in the centre of x₁, x₂, . . ., xₙ. 
• The next step is to find the difference ‘ dᵢ ’ between a and each of the xᵢ, that is, the deviation of ‘ a ’ from each of the xᵢ. i.e., dᵢ = xᵢ - a
• The third step is to find ‘ uᵢ ’ by dividing dᵢ by the class size h-for each of the xᵢ. i.e., uᵢ= dᵢ/h
• The next step is to find the product of uᵢ with the corresponding fᵢ, and take the sum of all the fᵢuᵢ.

The step-deviation method will be convenient to apply if all the dᵢ have a common factor. Now use the values in the formula below.

Mean, (x) = a + (Σfᵢuᵢ/Σfᵢ) × h

We know that, Class mark, xᵢ = (Upper class limit + Lower class limit) / 2

Class size, h = 3

Taking assumed mean, a = 75.5

From the table, we obtain Σfᵢ = 30 and Σfᵢuᵢ = 4

Mean, (x) = a + (Σfᵢuᵢ/Σfᵢ) × h

x = 75.5 + (4/30 × 3)

x = 75.5 + 2/5

= 75.5 + 0.4

= 75.9

Thus, for the given problem, the mean heartbeat per minute for these women is 75.9

☛ Check: NCERT Solutions Class 10 Maths Chapter 14

Video Solution:

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.

NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Question 4

Summary:

Thirty women were examined in a hospital by a doctor and the number of heartbeats per minute were recorded and summarised as follows. The mean heartbeats per minute for the thirty women examined in a hospital by a doctor is found using the step deviation method which is 75.9.

☛ Related Questions:

• In a retail market, fruit vendors were selling mangoes kept in packing boxes. These boxes contained varying number of mangoes. The following was the distribution of mangoes according to the number of boxes. Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?
• The table below shows the daily expenditure on food of 25 households in a locality. Find the mean daily expenditure on food by a suitable method.
• To find out the concentration of SO2 in the air (in parts per million, i.e., ppm), the data was collected for 30 localities in a certain city and is presented below: Find the mean concentration of SO2 in the air.
• A class teacher has the following absentee record of 40 students of a class for the whole term. Find the mean number of days a student was absent. We will solve this question by assumed mean method.