EX 13.3 (Question: 4)

EX 13.3 (Question: 4) The lengths of 40 leaves of a plant are measured correct to the nearest millimetre, and the data obtained is represented in the following table : Length (in mm) Number of leaves 118 - 126 3 127 - 135 5 136 - 144 9 145 - 153 12 154 - 162 5 163 - 171 4 172 - 180 2

Solution: Total number of neon lamps = 40 = "n/2" = 20. Cumulative frequency just greater than 20 = 29 So, the median class is 145 – 153Here, Lower boundary 𝑙=3000 Cumulative frequency before median class 𝑐𝑓=17 Frequency of median class 𝑓=12 Class width ℎ=9Using formula: Median = 𝑙 + ( "n/2−c𝑓" /"𝑓" )"×h" Where: 𝑙 = 144.5, c𝑓 = 17, 𝑓 = 12, ℎ = 9. Median = 144.5 + ("(20−17 " /12)"× 9" "=" 144.5 + 3/12 "×9" "=" 144.5 + 2.25 =146.75 mm Median length of the leaves = 146.75 mm

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