# 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 d_{i }have a common factor.

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

The first step is to select one among the x_{i} as the assumed mean and named it by ‘a’. Also, to further reduce our calculation work, we may take ‘a’ to be that x_{i} which lies in the centre of x_{1}, x_{2}, . . ., x_{n}. So, we can choose a.

The next step is to find the difference ‘ d_{i} ’ between a and each of the x_{i}, that is, the deviation of ‘ a ’ from each of the x_{i}. i.e., d_{i} = x_{i} - a

The third step is to find ‘ u_{i} ’ by dividing d_{i} and class size h-for each of the x_{i}. i.e., u_{i}= d_{i}/h

The next step is to find the product of u_{i} with the corresponding f_{i}, and take the sum of all the f_{i}u_{i}

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

Mean, (x) = a + (Σf_{i}u_{i}/Σf_{i}) × h

We know that, Class mark, x_{i} = (Upper class limit + Lower class limit) / 2

Class size, h = 3

Taking assumed mean, a = 75.5

From the table, we obtain Σf_{i} = 30 and Σf_{i}u_{i} = 4

Mean, (x) = a + (Σf_{i}u_{i}/Σf_{i}) × 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

**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:

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

The mean heartbeats per minute for the thirty women examined in a hospital by a doctor is 75.9