Find the missing frequency given that the median of the distribution is 1504. Life in hours 950 – 1150 1150 – 350 1350 – 1550 1550 – 1750 1750 – 1950 1950 – 2150 No. of bulbs 20 43 100 – 23 13

Let x be the missing frequency of the class 1550 – 750. Life in hours No. of bulbs (f) Less than Cumulative frequency(c.f.) 950 – 1150 20 20 1150 – 1350 43 63 1350 – 1550 100 163 1550 – 1750 x 163 + x 1750 – 1950 23 186 + x 1950 – 2150 13 199 + x Total 199 + x Here, N = 199 + x Given, Median (Q2) = 1504&there4; Q2 lies in the class 1350 – 1550&there4; L = 1350, f = 100, c.f. = 63, h = 200, `"2N"/(4)=(199+"x")/(2)` Q2= `"L"+"h"/"f"(("2N")/4 - "c.f.")` 1540 = `1350 + (200)/(100)((199 + "x")/2 - 63)` 1540 – 1350 = `2((199 + "x"-126)/2)` &there4; 154 = 199 + x – 126&there4; 154 = 73 + x&there4; x = 81

Find the missing frequency given that the median of distribution is 1504. Life in hours 950 – 1150 1150 –1350 1350 – 1550 1550 – 1750 1750 – 1950 1950 – 2150 No. of bulbs 20 43 100 – 23 13 - Mathematics and Statistics

Sum

Find the missing frequency given that the median of the distribution is 1504.

Life in hours	950 – 1150	1150 – 350	1350 – 1550	1550 – 1750	1750 – 1950	1950 – 2150
No. of bulbs	20	43	100	–	23	13

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Solution

Let x be the missing frequency of the class 1550 – 750.

Life in hours	No. of bulbs (f)	Less than Cumulative frequency (c.f.)
950 – 1150	20	20
1150 – 1350	43	63
1350 – 1550	100	163
1550 – 1750	x	163 + x
1750 – 1950	23	186 + x
1950 – 2150	13	199 + x
Total	199 + x