Height of students of Class X are given in the following frequency distribution:Height (in cm)150−155155−160160−165165−170170−175Number of students15820125Find the modal height. Also, find the mean height, Compare and interpret the two measures of central tendency.

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Filo · Accepted Answer

Here:Maximum class frequency =20The class corresponding to Maximum class frequency is the modal class.So, Modal class =160−165Lower limit =L=160Modal class size =h=5Frequency of class preceding the modal class =f0=8Frequency of the modal class =f1=20Frequency of class succeeding the modal =f2=12Mode formula is given by,Mode =L+(2f1​−f0​−f2​f1​−f0​​)×hMode =160+(2(20)−8−1220−8​)×12=160+12/20×5=163The modal height is 163 cm, which implies maximum number of students have model  height 163 cmHeightMid Point (xi​)No. of students (fi​)fi​xi​150−155152.5 152287.5155−160          157.5                   8                    1260160−165162.5203250165−170167.5122010170−175172.55862.5∑fi=60                                                     ∑fixi=9670We know,xˉ=∑i​f1​∑i​fi​xi​​=9670/60=161.17Mean is 161.17Thus, 161.7 cm is the average height of all the students.

Height (in cm)	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$
Number of students	$15$	$8$	$20$	$12$	$5$

Height (in cm)	$150 - 155$	$155 - 160$	$160 - 165$	$165 - 170$	$170 - 175$
Number of students	$15$	$8$	$20$	$12$	$5$

Height	Mid Point $(x_{i})$	No. of students $(f_{i})$	$f_{i} x_{i}$
$150 - 155$	$152.5$	$15$	$2287.5$
$155 - 160$	$157.5$	$8$	$1260$
$160 - 165$	$162.5$	$20$	$3250$
$165 - 170$	$167.5$	$12$	$2010$
$170 - 175$	$172.5$	$5$	$862.5$

Question Text	Height of students of Class $X$ are given in the following frequency distribution: Find the modal height. Also, find the mean height, Compare and interpret the two measures of central tendency.
Answer Type	Text solution:1
Upvotes	150

Text solutionVerified

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