Find the lower quartile, the upper quartile, the interquartile ra… - Vidyadip

Question

Find the lower quartile, the upper quartile, the interquartile range and the semi-interquartile range for the following frequency distributions:

Shoe size	5	6	7	8	9	10	11
Frequency	8	1	7	14	11	5	4

✓

Answer

Shoe size	Frequency (f)	Cumulative frequency
5	8	8
6	1	9
7	7	16
8	14	30
9	11	41
10	5	46
11	4	50

No. of terms $=50$
Lower Quartile $\left( Q _1\right)=\frac{n}{4}=\frac{50}{4}=12.5^{\text {th }}$ term $=7$
Upper Quartile $\left( Q _3\right)=\frac{n \times 3}{4}=\frac{50 \times 3}{4}=37.5^{\text {th }}$ term $=9$
Interquartile range $=Q_3-Q_1=9-7=2$
Semi-interquartile range $=\frac{Q_3-Q_1}{2}=\frac{9-7}{2}=1$
Hence, Lower quartile $=7$, upper quartile $=9$, interquartile range $=2$, semi-interquartile range $=1$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "[4 marks sum]" from Measures Of Central Tendency→Measures Of Central Tendency — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

Find the coordinates of the points of trisection of the line segment joining the points $(3, -3)$ and $( 6, 9).$

In a particular tax period $A $ to $Z$ Emporium purchased Silk Sarees worth $Rs. 5,00,000$ taxable at $12\%,$ Cotton Sarees worth $Rs. 8,00,000$ taxable at $5\%$ and Handloom Sarees worth $Rs. 3,00,000$ exempted from tax. In the same tax period it sold Silk Sarees worth $Rs. 12,00,000 ,$ Cotton Sarees worth $Rs. 16,00,000$ and Handloom Sarees worth $Rs. 7,00,000$. Silk Sarees worth $Rs. 40,000$ were returned due to manufacturing defect and Cotton Sarees worth $Rs. 60,000$ were returned due to loss of colour. Calculate the tax paid by the firm for this period.

If $q$ is the mean proportional between $p$ and $r$, prove that: $p^3-$ $3 q^2+r^2=q^4\left(\frac{1}{p^2}-\frac{3}{q^2}+\frac{1}{r^2}\right)$

QUESTION $A B$ and $C D$ are two chords of a circle such that $A B=6 cm, C D=12 cm$ and $A B \| C D$. If the distance between $A B$ and $C D$ is 3 cm , find the radius of the circle.

Show that each of the triangles whose vertices are given below are isosceles :
$(i)\ (8, 2), (5,-3)$ and $(0,0)$
$(ii)\ (0,6), (-5, 3)$ and $(3,1).$

An observer, 1.5m tall, is 28.5m away from a tower 30m high. Determine the angle of elevation of the top of the tower from his eye.

A straight line makes positive intercepts on the co-ordinates axes whose sum is 7 . If the line passes through the point $(-3,8)$, find its equation.

Plot the points $A (-2,0), B (4,0), C (1,4)$ and $D (-2,4)$ on a graph paper. Point D is reflected about the line $x=1$ to get the image E. Write the coordinates of E. Name the figure ABED.

Three vertices of a parallelogram ABCD taken in order are $A(3,6),B(5,10)$ and $C(3,2),$ find :
$(1)$ the co-ordinates of the fourth vertex D.
$(2)$ Length of diagonal BD.
$(3)$ equation of side AB of the parallelogram ABCD

In the following figure, AD and CE are medians of ΔABC. DF is drawn parallel to CE. Prove that :
(i) EF = FB,
(ii) AG : GD = 2 : 1