Mathematics

In a malaria epidemic, the number of cases diagnosed were as follows :
Date (July) Number
1 5
2 12
3 20
4 27
5 46
6 30
7 31
8 18
9 11
10 5
11 0
12 1
On what days do the mode, the upper and the lower quartiles occur ?

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Cumulative frequency distribution table :

Here, n = 206, which is even

Lower quartile = $\dfrac{n}{4}$ th term

= $\dfrac{206}{4}$ = 51.5 th term

From table,

It is observed the date of 38th term to 64th term is 4th july.

Upper quartile = $\dfrac{3n}{4}$ th term

= $\dfrac{3 \times 206}{4}$ = 154.5 th term

From table,

It is observed the date of 141st term to 171st term is 7th july.

From table,

5th july has the highest no. of cases diagnosed.

Hence, mode = 5th july, upper quartile = 7th july and lower quartile = 4th july.

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