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# 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.

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## 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.Number of mangoes 50

Click here👆to get an answer to your question ✍️ 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.Number of mangoes 50 - 52 53 - 55 56 - 58 59 - 61 62 - 64 Number of boxes 15 110 135 115 25 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose? Join / Login Class 11 >>Economics

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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.

Question

Number of mangoes 50−52 53−55 56−58 59−61 62−64

Number of boxes 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Medium Open in App

Updated on : 2022-09-05

Solution Verified by Toppr

Number of mangoes  Number of boxes  x

i ​ f i ​ x i ​ 50-52  15  51  765

53-55  110  54  5940

56-58  135  57  7695

59-61  115  60  6900

62-64  25  63  1575 Σf i ​ =400    Σf i ​ x i ​ =22875 x ˉ = Σf i ​ Σf i ​ x i ​ ​ = 400 22875 ​ =57.1875

Hence, the mean number of mangoes kept in a packing box is 57.1875.

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Mathematics NCERT Exercise 14.1 SIMILAR QUESTIONS

### The fruit vendor has apples packed in boxes. Each box contains different numbers of apples. The following was the distribution of apples according to the number of boxes. Find the mean number of Apples kept in a packing box using the direct method.

A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality.Find the mean number of plants per house.

Medium View solution > Number of plants 0−2 2−4 4−6 6−8 8−10 10−12 12−14 Number of houses 1 2 1 5 6 2 3

Which method did you use for finding the mean, and why?

In a retail market fruit vendor were selling mangoes in boxes. These boxes contained varying number of mangoes. The following was the distribution.

Medium View solution >

No.of mangoes  50−52 53−55

56−58 59−61 62−64

No. of boxes 15 110 135 115 25

Find the mean and median number of mangoes kept in a packing box.

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.

Medium View solution > No. of mangoes 50−52 53−55 56−58 59−61 62−64 No. of boxes 15 110 135 115 25

If mean number of mangoes kept in a pocket box. Which method of finding the mean did you choose?

Below is the given frequency distribution of words in an essay:

Medium View solution >

Number of Words         Number of Candidates

600−800 14 800−1000 22 1000−1200 30 1200−1400 18 1400−1600 16

Find the mean number of words written

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## Arithmetic Mean : Ungrouped Data

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## Arithmetic Mean : Grouped Data

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## Question 5 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. Number of mangoes 50 52 53 55 56 58 59 61 62 64 Number of boxes 15 110 135 115 25 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Question 5 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. Number of mangoes 50 52 53 55 56 58 59 61 62 64 Number of boxes 15 110 135 115 25 Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose? Mean for Ungrouped Data

Question 5 In... Question

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.

Number of mangoes 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64 Number of boxes 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

Open in App Solution Number of mangoes Number of boxes 50 − 52 15 53 − 55 110 56 − 58 135 59 − 61 115 62 − 64 25

We may observe that class intervals are not continuous. There is a gap of

1

between two class intervals. So we have to add

1 2

to upper class limit and subtract

1 2

from lower class limit of each interval.

The class mark ( x i )

may be obtained by using the relation:

x i =

Upper class limit + lower class limit

2 Class size h of this data = 3

Since, the given data is large, we will use Assumed Mean Method to find the mean. This method helps in reducing the calculations and results in small numerical values. We will choose the assumed mean

( a )

in such a way so that the the value obtained in

d i

,cancel out each other.

Now, taking 57 as assumed mean ( a ) ; we may calculate d i , u i , f i u i as following – Class interval f i x i d i = x i − 57 f i d i 49.5 − 52.5 15 51 − 6 − 90 52.5 − 55.5 110 54 − 3 − 330 55.5 − 58.5 135 57 0 0 58.5 − 61.5 115 60 3 345 61.5 − 64.5 25 63 6 150 Total 400 75

Now, we may observe that:

∑ f i = 400 ∑ f i d i = 75 Mean ¯ x = a + ( ∑ f i d i ∑ f i ) = 57 + 75 400 = 57 + 0.1875 = 57.1875 = 57.2

Clearly, mean number of mangoes kept in a packing box is

57.2 . Suggest Corrections 107 Video Solution NCERT - Grade 10 - Mathematics - Statistics - Q5

MATHEMATICS

05:24 Min | 672 Views

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Q. In a retail market , fruit vendors were selling mangoes kept in packed boxes. These boxes contained different number of mangoes. The following was the distribution of mangoes according to the number of boxes ?

Number of mangoes 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64 Number of boxes 15 110 135 115 25

Find the mean number of mangoes using step-deviation method.

Q.

Consider the following distribution of the number of mangoes being packed in cardboard boxes where these boxes contain varying number of mangoes. Find the mean number of mangoes kept in a packing box using assumed mean method.

N u m b e r o f M a n g o e s 50 − 52 53 − 55 56 − 58 59 − 61 62 − 64 N u m b e r o f b o x e s 15 110 135 115 25

Can the assumed mean be 60?

Q. 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.

Number of mangoes: 50−52 53−55 56−58 59−61 62−64

Number of boxes: 15 110 135 115 25

Find the mean number of mangoes kept in a packing box. Which method of finding the mean did you choose?

EXPLORE MORE

Mean for Ungrouped Data

Standard X Mathematics

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## Ex 14.1, 5

Ex 14.1, 5In 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 th Check sibling questions

## Ex 14.1, 5 - Chapter 14 Class 10 Statistics (Term 2)

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### Transcript

Ex 14.1, 5 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? Since there is a gap of 1 between intervals We add ½ to upper limit, and subtract ½ to lower limit Now, let’s find mean Mean(𝑥 ̅) = a + h × (∑▒𝒇𝒊𝒖𝒊)/(∑▒𝒇𝒊) Where a = Assumed mean h = Class interval = 57 = 52.5 – 49.5 = 3 Also, ∑▒𝒇𝒊 = 400 ∑▒𝒇𝒊𝒖𝒊 = 25 Putting values in formula Mean(𝒙 ̅) = a + h × (∑▒𝒇𝒊𝒖𝒊)/(∑▒𝒇𝒊) 𝑥 ̅ = 57 + 3 × 25/400 𝑥 ̅ = 57 + 0.1875 𝑥 ̅ = 57.1875 𝒙 ̅ = 57.19 Thus, Mean number of boxes is 57.19 We chose this method because calculation was easier

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