Marks 10 20 30 40 50 No. of Students 4 7 13 8 6 1) Write the formula of Q1 and Q3. 2) Find out the median of the above data? 3) Find out the cumulative frequency of the last value in the above data. 4) Find out the value of 'n' in the above data - Economics

QUESTION

Answer the following questions on the basis of the given data :

Marks	10	20	30	40	50
No. of Students	4	7	13	8	6

1) Write the formula of Q₁ and Q₃.

2) Find out the median of the above data?

3) Find out the cumulative frequency of the last value in the above data.

4) Find out the value of 'n' in the above data

Sum 

SOLUTION

Marks	No. of Students	cf
10	4	4
20	7	11
30	13	24
40	8	32
50	6	38
	N = 38

1. Formula of Q₁

Q₁ = Size of 1${\displaystyle {\left(\frac{n+1}{4}\right)}^{\text{th observation}}}$

Formula of Q₃

Q₃ = Size of 3${\displaystyle {\left(\frac{n+1}{4}\right)}^{\text{th observation}}}$

2. Median = Q₂

Median = Q₂ = Size of 2${\displaystyle {\left(\frac{n+1}{4}\right)}^{\text{th observation}}}$

= Size of 2${\displaystyle {\left(\frac{38+1}{4}\right)}^{\text{th observation}}}$

= Size of 2${\displaystyle {\left(\frac{40}{4}\right)}^{\text{th observation}}}$

= Size of 2 (9.75)^{th observation}

= Size of 19.5^{th observation}

= Size of 19.5^{th observation} lies in cf 24

Hence, quartile value = 30 marks. 

3. The cumulative frequency of the last value in the above data is 38.

4. The value of 'n' in the above data is 38.