Ex.3.1 Q9 Data Handling - NCERT Maths Class 7

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Question

The heights of the \(10\) girls were measured in cm and the results are as follows:
\(135, 150, 139, 128, 151, 132, 146, 149, 143, 141.\)

(i) What is the height of the tallest girl?

(ii) What is the height of the shortest girl?

(iii) What is the range of the data?

(iv) What is the mean height of the girls?

(v) How many girls have height more than the mean height?

Text Solution

What is known?

Height of the \(10\) girls

What is unknown?

(i) Height of the tallest girl (ii) Height of the shortest girl (iii). Range of the data (iv) Mean height

Range= Height of tallest girl – Height of the shortest girl

Mean\(=\)\(\begin{align}\frac{\text{sum of all heights}\left(\text{in mm }\right)}{\text{Number of girl}s}\end{align}\)

Steps:

(i) The height of the tallest girl \(=151 \rm\,cm\)

(ii) The height of the shortest girl \(= 128 \rm \,cm\)

(iii) Range of the data \(= 151 – 128 =\) \(23\rm\, cm\)

Total number of girls \(= 10\)

Measurement of the heights of 10 girls \(= 135, 150, 139, 128, 151, 132, 146, 149, 143, 141.\)

\[\begin{align}{\text{Mean height of the girls}} &= \frac{{135 + 150 + 139 + 128 + 151 + 132 + 146 + 149 + 143 + 141}}{{10}}\\& = \frac{{1414}}{{10}}\\ &= 14.14\;{\rm{cm}}\end{align}\]

Five girls have heights more than the mean height i.e.: \(150, 151, 146, 149, 143.\)

  
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