Question

CASE STUDY: 2 Apples are most widely planted and are commercially the most important fruit crop in Jammu and Kashmir. The cultivation of apple crop in Jammu and Kashmir shows particular interest for a number of reasons. In terms of both area and production, apple is very beneficial. Horticultural department has tasked their statistical officer to create a model for farmers to be able to predict their produce output based on various factors. A box containing 250 apples was opened and each apple was weighed. The distribution of the masses of the apples is given in the following table: Mass (in grams) 80-100 100-120 120-140 140-160 160-180 Frequency 20 60 X 40 60 (i) How many apples are in the range 120-140 mass ? (ii) What is the mean mass of the apples? (iii) What is the lower limit of the median class? (iv) What is the median mass of the apples? (v) What is the modal class of the apples?

Answer 1

Answer:

i ans (1) 40

ii ans (1) 131.4g

iii ans (4) 140

iv ans (5) 132g

v ans (1) 122.33g

Answer 2

Answer:

(i) There are 70 apples in the range 120 - 140 mass.

(ii) The mean mass of the apples is 135 gram

(ii) The lower limit of the median class = 120

(iv) The median mass is 132.86 gram

(v) The modal class is 120 - 140

Step-by-step explanation:

The given data:

weight               frequency(f)            CF         Class mark(x)                      fx

80 - 100                           20             20            90                               1800

100 - 120                           60            80             110                              6600

120 - 140                      x = 70            150            130                              9100

140 - 160                           40           190             150                             6000

160 - 180                           60           250            170                             10200

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                                      250                                                              33700

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(i) Given that the total apples are 250

=> 20 + 60 + x + 40 + 60 = 250

=> 180 + x = 250

=> x = 250 - 180

=> x = 70

Therefore, there are 70 apples in the range 120 - 140 mass.

(ii) We know that Mean  = $\frac{\sum fx}{\sum f}$

                                       = $\frac{33700}{250}$

                                       = 134.80

                                       ≈ 135

Therefore, the mean mass of the apples is 135 gm

(iii) To find the median class, we write the cumulative frequency of the data.

As $\sum f$ = 250 = even,

we calculate $\sum f$ /2 = 250/2 = 125

As 125 will lie in the interval 120 - 140, it will be the median class.

Therefore, the lower limit of the median class = 120

(iv) The median class is 120 - 140

We know that Median = l + $\frac{\frac{n}{2}-cf}{f}$ * h

where, l = lower limit of the median class

          n = number of observations

          f = frequency of median class

         cf = cumulative frequency of the class before the median class

          h = size of the class interval

Therefore, here,

Median = 120 +$\frac{\frac{250}{2}-80}{70}$ * 20

         = 120 + $\frac{125-80}{70}$ * 20

         = 120 + $\frac{45}{70}$  * 20

         = 120 + 12.857

         = 132.86

Therefore, the median mass is 132.86 gram

(v) We know that Modal class is the class with highest frequency

Here as 70 is the highest frequency, the modal class will be 120 - 140

Therefore, the modal class is 120 - 140