Question
An investigation of 23713 households was made in an urban and rural mixed locality. Of these 1618 were farmers, 2015 well to do and 770 families were having at least one graduate. Of these graduate families 335 were those of farmers and 428 were well to do; also 587 well to do families were those of farmers and out of them only 156 were having at least one graduate. Obtain all the ultimate class frequencies.
Answer :
Word Count : 722
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We are given a survey of 23,713 households classified into three categories: 1. Farmers (\( F \)) = 1,618 2. Well-to-do (\( W \)) = 2,015 3. Families having at least one graduate (\( G \)) = 770 Additionally, we have the following data: - Graduate farmers (\( F \cap G \)) = 335 - Graduate well-to-do families (\( W \cap G \)) = 428 - Well-to-do farmers (\( F \cap W \)) = 587 - Well-to-do farmers who also have a graduate (\( F \cap W \cap G \)) = 156 We need to determine all the ultimate class frequencies, meaning the number of families in each possible category combination. --- ### Step 1: Define Variables Let: - \( _____ ______ _________ __________ _______ _____ _______ _____.
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