Question 2 - Case Based Questions (MCQ) - Chapter 13 Class 10 Statistics

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Question Electricity energy consumption is the form of energy consumption that uses electric energy. Global electricity consumption continues to increase faster than world population, leading to an increase in the average amount of electricity consumed per person (per capita electricity consumption). A survey is conducted for 56 families of a Colony A. The following tables gives the weekly consumption of electricity of these families.The similar survey is conducted for 80 families of Colony B and the data is recorded as below:Refer to data received from Colony A Question 1 The median weekly consumption is (a) 12 units (b) 16 units (c) 20 units (d) None of theseMedian = l + (𝑵/𝟐 −𝒄𝒇)/𝒇 × h Here, 𝑵/𝟐=56/2= 28 ∴ 10 – 20 is the median class And, l = lower limit of median class = 10 h = class-interval = 10 cf = cumulative frequency of the class before median class = 16 f = frequency of the median class = 12 Putting values in formula Median = l + (𝑁/2 −𝑐𝑓)/𝑓 × h = 10 + (𝟐𝟖 −𝟏𝟔)/𝟏𝟐 × 10 = 10 + 12/12 × 10 = 10 + 10 = 20 So, the correct answer is (c) Refer to data received from Colony A Question 2 The mean weekly consumption is (a) 19.64 units (b) 22.5 units (c) 26 units (d) None of theseMean(𝑥 ̅) = (∑▒𝒇𝒊𝒙𝒊)/(∑▒𝒇𝒊) = 1100/56 = 19.64 units So, the correct answer is (a) Refer to data received from Colony A Question 3 The modal class of the above data is (a) 0 – 10 (b) 10 – 20 (c) 20 – 30 (d) 30 – 40 Modal class is class with highest frequency Since 20 – 30 has highest frequency 18 ∴ It is the modal class So, the correct answer is (c) Refer to data received from Colony B Question 4 The modal weekly consumption is (a) 38.2 units (b) 43.6 units (c) 26 units (d) 32 units Mode = l + (𝒇𝟏 − 𝒇𝟎)/(𝟐𝒇𝟏 − 𝒇𝟎 − 𝒇𝟐) × h Modal class = Interval with highest frequency = 40 - 50 where l = lower limit of modal class = 40 h = class-interval = 10 f1 = frequency of the modal class = 40 f0 = frequency of class before modal class = 20 f2 = frequency of class after modal class = 5 Putting values in formula Mode = l + (𝑓1 −𝑓0)/(2𝑓1 −𝑓0 −𝑓2) × h = 40 + (𝟒𝟎 −𝟐𝟎)/(𝟐(𝟒𝟎) −𝟐𝟎 −𝟓) × 10 = 40 + 20/(80 −25) × 10 = 40 + 20/55 × 10 = 40 + 40/11 = 40 + 3.6 = 43.6 So, the correct answer is (b) Refer to data received from Colony B Question 5 The mean weekly consumption is (a) 15.65 units (b) 32.8 units (c) 38.75 units (d) 48 unitsMean(𝑥 ̅) = (∑▒𝒇𝒊𝒙𝒊)/(∑▒𝒇𝒊) = 3100/80 = 38.75 So, the correct answer is (c)