Find the mean of the following frequency distribution by the step… - Vidyadip

Question

Find the mean of the following frequency distribution by the step deviation method :

$\text{Class}$	$100-110 $	$110-120 $	$120-130 $	$130-140 $	$140-150 $
$\text{Frequency}$	$15$	$18$	$32$	$25$	$10$

✓

Answer

$\text{Class Interval}$	$x_i$	$f_i$	$A = 35.5 d = x - A$	$f_id$
$100-110$	$105$	$15$	$-2$	$-30$
$110-120$	$115$	$18$	$-1$	$-18$
$210-130$	$A=125$	$32$	$ 0$	$0$
$310-140$	$135$	$25$	$1$	$25$
$140-150$	$145$	$10$	$2$	$20$
$\text{Total}$		$100$		$-3$

$ A =125 \text { and } h _{ i }=10$
$\bar{x}=A+ h \times \frac{\Sigma f_i u }{\Sigma f_i}$
$\bar{x}=125+10 \times \frac{-3}{100}$
$\bar{x}=125-0.3$
$\bar{x}=124.70$
$\therefore \text { Mean }=124.70$

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 "[5 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

There is a building of height 7 m next to a cable tower of unknown height. From the top of the building, the angle of elevation of the top of the tower is $60^{\circ}$ and the angle of depression to the foot of the tower is $45^{\circ}$. Find the height of the cable tower.

If A and B are complementary angles, prove that:$\frac{\sin A+\sin B}{\sin A-\sin B}+\frac{\cos B-\cos A}{\cos B+\cos A}=\frac{2}{2 \sin ^2 A-1}$

Given that $x – 2$ and $x + 1$ are factors of $f(x) = x^3 + 3x^2 + ax + b;$ calculate the values of $a$ and $b.$ Hence, find all the factors of $f(x).$

A shopkeeper buys a certain number of books for Rs 960. If the cost per book was Rs 8 less, the number of books that could be bought for Rs 960 would be 4 more. Taking the original cost of each book to be Rs x, write an equation in x and solve it to find the original cost of each book.

Mrs. Kulkarni invests Rs.1, 31,040 in buying Rs.100 shares at a discount of 9%. She sells shares worth Rs.72,000 at a premium of 10% and the rest at a discount of 5%. Find her total gain or loss on the whole.

Solve the following linear in-equation and graph the solution set on a real number line:
$4 \frac{3}{4} \geq x +\frac{5}{6}>\frac{1}{3}, x \in R$

Draw a circle with centre O and radius 2.5 cm. Take a point P at a distance of 6 cm from the centre. Using ruler and compasses only construct the tangents to the circle from the point P.

If $ax^3 + 3x^2 + bx – 3$ has a factor $(2x + 3)$ and leaves remainder $– 3$ when divided by $(x + 2)$, find the values of a and b. With these values of a and b, factorise the given expression.

A chord of a length $16.8 \ cm$ is at a distance of $11.2 \ cm$ from the centre of a circle . Find the length of the chord of the same circle which is at a distance of $8.4 \ cm$ from the centre.

From an aeroplane vertically above a straight horizontal road, the angles of depression of two consecutive milestone on opposite sides of the aeroplane are observed to be $\alpha$, and $\beta$. Show that the height in miles of aeroplane above the road is $\frac{\tan \alpha \tan \beta}{\tan \alpha+\tan \beta}$.