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?
Solution:
Here, the given class interval is not continuous. First, we have to make it continuous. There is a gap of 1 between two class intervals. Therefore, half of the gap i.e., 0.5 has to be added to the upper-class limit and 0.5 has to be subtracted from the lower-class limit of each interval.
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 = 57
From the table, we obtain, Σfᵢ = 400 abd Σfᵢuᵢ = 25
Mean, (x) = a + (Σfᵢuᵢ/Σfᵢ) × h
= 57 + (25/400) × 3
= 57 + 1/16 × 3
= 57 + 3/16
= 57 + 0.19
= 57.19
The mean number of mangoes kept in a packing box are 57.19.
☛ Check: NCERT Solutions Class 10 Maths Chapter 14
Video Solution:
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?
NCERT Solutions for Class 10 Maths Chapter 14 Exercise 14.1 Question 5
Summary:
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.The mean number of mangoes kept in a packing box by the fruit vendors in a retail market is 57.19 using step deviation method.
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