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Question : Direction: Study the table and answer the question.

Height (in cm) Number of girls
less than 140 4
less than 145 11
less than 150 29
less than 155 40
less than 160 46
less than 165 51

The average height (in cm) of the girls whose heights are 155 cm and above is about:

Option 1: 158.7

Option 2: 159.8

Option 3: 160.4

Option 4: 162.6


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 16th Jan, 2024

Correct Answer: 159.8


Solution : As per the given table,
There are 40 girls with a height of less than 155 cm.
The number of girls with a height of 155 cm and above = 51 – 40 = 11
Assuming that the heights of the girls are uniformly distributed in each interval.
We can estimate the average height of these 11 girls.
6 girls are in the interval 155 cm to 160 cm.
$\therefore$ The average height in this interval = $\frac{155 + 160}{2}$ = 157.5 cm
5 girls are in the interval 160 cm to 165 cm.
$\therefore$ The average height in this interval = $\frac{160 + 165}{2}$ = 162.5 cm
The average height of the girls whose heights are 155 cm and above = $\frac{6 × 157.5 + 5×162.5}{11}$ = 159.8 cm
Hence, the correct answer is 159.8.

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