Q) The following table gives the distribution of the life time of 400 neon lamps.

Find the median lifetime of a lamp.

Ans: Let’s re-organize the data in the frequency table to find out each part:

To find the median, we need to identify middle value of the data. Let’s rearrange the data:

• First, we need to find the cumulative frequency in the frequency table to find the median. Its shown in last column.
• Next, Total number of sub-divisions or Sum of the frequencies = 400. It shown in the last row of middle column.
• Next, we need to identify Median Class. Since the Median class is the class where the cumulative frequency crosses 50% of the half the total number of sub-divisions, here in the table, Cumulative frequency of 216 is crossing 50% of frequency i.e. 200, at class “3000 – 3500”. Hence, our Median class = 3000 – 3500
• Next, To find the median, we use the formula:

Median = L+x h

Here:

L = Lower boundary of the median class = 3000

n = Total number of sub-divisions = 400

= Cumulative frequency of the class before the median class = 130

f = Frequency of the median class = 86

h = Class width = 3500 – 3000 = 500

hence, the Median = 3000 + x 500

⇒ 3000 + [(200 – 130)] x

⇒ 3000 +

⇒ 3000 + 406.98

⇒ 3406.98 hours

Therefore, Median life of the lamp is 3,406.98 hours.

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