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Heights of students of Class X are given in the following frequency distribution:

Height (in cm)
150-155
155-160
160-165
165-170
170-175
No. of students
15
8
20
12
5

Then what is the mean height?

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159.17 cm

160.17 cm

162.17 cm

161.17 cm

answer is D.

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Detailed Solution

The given heights of students of Class X:

Height (in cm)	150-155	155-160	160-165	165-170	170-175
No. of students	15	8	20	12	5

The frequency distribution table will be:

Height (in cm)	Frequency, $f_{i}$	Mid-value, $x_{i}$	$f_{i} x_{i}$
150-155	15	152.5	2287.5
155-160	8	157.5	1260
160-165	20	162.5	3250
165-170	12	167.5	2010
170-175	5	172.5	862.5
	Σ $f_{i}$ = 60		Σ $f_{i} x_{i}$ =9670

Formula used for mean:

M e a n = ∑ f i x i ∑ f i

Substituting the values:

M e a n = ∑ f i x i ∑ f i M e a n = 976060 M e a n = 161.17

Therefore, the mean of the given data is 161.17.
Thus, the correct option is option 4.

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