Find the arithmetic mean (correct to the nearest whole-number) by… - Vidyadip

Question

Find the arithmetic mean $($correct to the nearest whole$-$number$)$ by using step$-$deviation method.

$x$	$5$	$10$	$15$	$20$	$25$	$30$	$35 $	$40$	$45$	$50$
$f$	$20$	$43$	$75$	$67$	$72$	$45$	$39$	$9$	$8$	$6$

✓

Answer

Let the assumed mean $A = 30$

$x$	$f$	$d=x-A$	$t=(x-A)/(i)=(x-30)/(5)$	$ft$
$5$	$20 $	$-20$	$-5$	$-100$
$10$	$43$	$-15$	$-3$	$-129$
$15$	$75$	$-10$	$-2$	$-150$
$20$	$67$	$-5$	$-1$	$-67$
$A=25$	$72$	$0$	$0$	$0$
$30$	$45$	$5$	$1$	$45$
$35$	$39$	$10$	$2$	$78$
$40$	$9$	$15$	$3$	$27$
$45$	$8$	$20$	$4$	$32$
$50$	$6$	$25$	$5$	$30$
	Sigma $f=384$			Sigma $ft=-234$

$\therefore \text { Mean }= A +\frac{\Sigma f t}{\Sigma f} \times i$
$=30+\frac{(-598)}{384} \times 5$
$=30-\frac{299}{192} \times 5$
$=30-\frac{1495}{192}$
$=\frac{5760-1495}{192}$
$=\frac{14265}{192}$
$=22.21$
$=22$

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 Measure of Central Tendency (Mean, Median, Quartiles and Mode)→Measure of Central Tendency (Mean, Median, Quartiles and Mode) — all question types→Mathematics STD 10 question papers→ICSE Board STD 10 question papers→ICSE Board question paper generator→

Similar questions

The mean of the following distribution is $21 \frac{1}{7}$. find the value of $f$

$C.I$	$0-10 $	$10-20$	$20-30$	$30-40$	$40-50$
Freq	$8$	$22$	$31$	$f$	$2$

Of the two trees are on either side of a river, one of them is 50m high. From the top of this tree the angles of depression of the top and the foot of the other tree are 30° and 60° respectively. Find the width of the river and the height of the other tree.

Prove that the points $(a , b) , (a + 3 , b + 4) , (a - 1 , b + 7)$ and $(a - 4 , b + 3)$ are the vertices of a parallelogram.

Draw an ogive for the following :

Class Interval	100-150	150-200	200-250	250-300	300-350	350-400
Frequency	10	13	17	12	10	8

The mean of the folowing is $62.8$ and the sum of all the frequencies is $50$. find the missing frequency $f_1$ and $f_2$

Class	0-20	20-40	40-60	60-80	80-100	100-120
Freq	5	$f_1$	10	$f_2$	7	8

In the figure, ABCD is a cyclic quadrilateral with BC = CD. TC is tangent to the circle at point C and DC is produced to point G. If ∠BCG = 108° and O is the centre of the circle, find : Angle BCT

In a square ABCD, its diagonal AC and BD intersect each other at point O. The bisector of angle DAO meets BD at point M and bisector of angle ABD meets AC at N and AM at L. Show that - ∠ BAM = ∠ BMA

Find two numbers whose mean proportional is 16 and the third proportional is 128.

The cost of a scooter depreciated by Rs 5100 during the second year and by Rs 4,335 during the third year. Calculate
The original cost of the scooter.

Find the values of $m$ and $n$ when the polynomial $f(x)=x^3-2 x^2+m x+n$ has a factor $(x+2)$ and leaves a remainder 9 when divided by $( x +1$ ).