Ex.14.3 Q5 Statistics Solution - NCERT Maths Class 9

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Question

The following table gives the life times of \(400\) neon lamps:

Life time (in hours) Number of lamps
\(300 - 400\) \(14\)
\(400 - 500\) \(56\)
\(500 - 600\) \(60\)
\(600 - 700\) \(86\)
\(700 - 800\) \(74\)
\(800 - 900\) \(62\)
\(900 - 1000\) \(48\)

(i) Represent the given information with the help of a histogram.

(ii) How many lamps have a life time of more than \(700\) hours?

Text Solution

 

What is known?

Life times of \(400\) neon lamps.

What is Unknown?

(i) A histogram representation for the given data.

(ii) Number of lamps that have a lifetime of more than \(700\) hours.

Reasoning:

The given data can be represented with the help of a histogram as above:

  1. Represent the ‘lifetime (in hours) in \(x\)-axis.
  2. Represent the ‘number of lamps’ in \(y\)-axis.
  3. Class intervals are continuous.
  4. Take “\(1\,\rm unit = 10\,\rm lamps\)” on \(y\)-axis as the lowest value of frequency is \(14\) and highest \(86.\)
  5. Also since the first interval is starting from \(300\) and not ‘\(0\)’, we show it by marking a ‘kink’ or a break on the \(x\)-axis.

Steps:

From the above graph, it can be concluded that: The number of neon lamps having their lifetime more than \(700\) is under class intervals “\(700 – 800, 800 – 900, 900 – 1000\)”.

Hence, their corresponding frequencies when added up will be \((72 + 62 + 48) 184\) lamps.

  
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