Question

Decide whether mean or mode is a better representative value in the following situations.
${\text{(i)}}$ A shopkeeper, who sells toothpaste tubes of different sizes, wants to decide which size to be ordered more.
${\text{(ii)}}$ An invigilator wants to bring sufficient numbers of additional papers to the examination hall.
${\text{(iii)}}$ Preparation of the number of laddus for a marriage
${\text{(iv)}}$ For finding the favorite cricketer in a class

Answer 1

Hint: We will check each condition and see what fits better for the given statement. We have to check the mean case and mode case for each of the options and select the best representative for each of the options.

Complete step-by-step solution:
${\text{(i)}}$A shopkeeper has to sell toothpaste of different sizes to his customer, to find the toothpaste he should keep in his store, he should use:
Mode: Since the shopkeeper has to sell a greater number of toothpaste tubes, he should select the one which most people buy therefore he should go with the mode of the toothpaste sizes. If he uses the mean then he will get the average value of the toothpaste which is not a good measure since the toothpaste is sold as a whole in a specific size.
${\text{(ii)}}$ An invigilator wants to bring sufficient number of additional papers to the examination hall, she should use:
Mean: The invigilator should check what is the average number of sheets required by the students in the examination hall therefore should bring a mean number of additional papers to the examination hall. If the invigilator uses the mode then he will find what number of pages is used by most students for the examination which will result in her bringing fewer numbers of pages for the students who require papers which are more than the mode.
${\text{(iii)}}$ Preparation of the number of laddus for a marriage
Mean: Since median will let us know the average number of laddus consumed by the people attending the marriage. If the mode is used, it will find what number of laddus are eaten by most of the people, since some people would eat less laddus than the mode and some higher, there won’t be sufficient laddus for everyone.
${\text{(iv)}}$ For finding the favorite cricketer in a class
Mode: Since it will find the cricketer who is the favorite of most in the class. Also the favorite cricketer is a nominal category which is not represented using numbers; therefore the mode has to be used.

Note: Mode is to be used when the given distribution is nominal, which implies that the class or category is not based on numbers for example: city, age, gender etc.
Mean is the most commonly used measure of central tendency and it is usually considered to be the measure of it. Mean should not be used when the data is non-numeric or when there are extreme values in the distribution.