Name: Introduction to the Statistics
Uploaded: 2019-07-19
Duration: 4 min 50 s
Description: Statistics is a branch of Mathematics. In this video, we will learn the meaning of statistics and the classification of data. Let's watch this useful video t...

Question

Find the arithmetic mean of the following frequency distribution:

Marked below	$10$	$20$	$30$	$40$	$50$	$60$	$70$	$80$	$90$	$100$
No. of students	$12$	$22$	$35$	$50$	$70$	$86$	$97$	$104$	$109$	$115$

Accepted Answer

The given data may be written as:

Class interval $0 - 10$ $10 - 20$ $50$ $30 - 40$ $40 - 50$ $50 - 60$ $12$ $70 - 80$ $80 - 90$ $90 - 100$

No. of students $12$ $22 - 12 = 10$ $35 - 22 = 13$ $50 - 35 = 15$ $70 - 50 = 20$ $86 - 70 = 16$ $97 - 86 = 11$ $104 - 97 = 7$ $109 - 104 = 5$ $10$

We prepare the table as below:

Class interval Frequency $(f_{i})$ Class Mark $(x_{i})$ Deviations $d_{i} = x_{i} - 55$ $50$ $f_{i} u_{i}$

$0 - 10$ $12$ $\frac{0 + 10}{2} = \frac{10}{2} = 5$ $5 - 55 = - 50$ $\frac{- 50}{10} = - 5$ $- 60$

$10 - 20$ $10$ $15$ $- 40$ $- 4$ $- 40$

$20 - 30$ $13$ $25$ $- 30$ $- 3$ $- 39$

$30 - 40$ $15$ $35$ $- 20$ $- 2$ $- 30$

$40 - 50$ $20$ $45$ $- 10$ $- 1$ $- 20$

$50 - 60$ $16$ $55 = a$ $0$ $0$ $0$

$60 - 70$ $11$ $65$ $10$ $1$ $11$

$70 - 80$ $7$ $75$ $20$ $2$ $14$

$80 - 90$ $5$ $85$ $30$ $3$ $15$

$90 - 100$ $6$ $95$ $40$ $4$ $24$

$\sum f_{i} = 115$ $\sum f_{i} u_{i} = - 125$

Let, the assumed mean $a = 55$ and class size $h = 10$ , then we have,

Mean $\bar{x} = a + \frac{Σ f_{i} u_{i}}{Σ f_{i}} \times h$ $= 55 + \frac{- 125}{115} \times 10 = 55 - 10.87 = 44.13 (approx)$

Hence, the arithmetic mean is $44.13$ .

Daily wages (in $₹$ )	$100 - 120$	$120 - 140$	$140 - 160$	$160 - 180$	$180 - 200$
No. of workers	$12$	$- 40$	$8$	$20 - 30$	$10$

Life time (in $hours$ )	$300 - 399$	$400 - 499$	$500 - 599$	$600 - 699$	$700 - 799$
Frequency	$14$	$46$	$58$	$76$	$68$

Life time (in $hours$ )	$800 - 899$	$900 - 999$	$1000 - 1099$	$1100 - 1199$
Frequency	$62$	$48$	$22$	$6$

Class interval	$0 - 4$	$4 - 8$	$8 - 12$	$12 - 16$	$16 - 20$	$20 - 24$	$24 - 28$	$28 - 32$	$32 - 36$	$36 - 40$
Frequency	$0$	$7$	$9$	$17$	$12$	$10$	$6$	$3$	$1$	$0$

Age (in years)	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$
Number of patients	$6$	$11$	$18$	$24$	$17$	$13$	$5$

Find the arithmetic mean of the following frequency distribution:

Marked below $10$ $20$ $30$ $40$ $50$ $60$ $70$ $80$ $90$ $100$

No. of students $12$ $22$ $35$ $50$ $70$ $86$ $97$ $104$ $109$ $115$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Marks	$0 - 10$	$- 30$	$20 - 30$	$30 - 40$	$40 - 50$
Number of students	$20$	$24$	$40$	$36$	$16$

Class interval	$0 - 20$	$20 - 40$	$40 - 60$	$60 - 80$
Frequency	$15$	$6$	$18$	$10$

Class interval	$10 - 14$	$14 - 18$	$18 - 22$	$22 - 26$	$26 - 30$	$30 - 34$	$34 - 38$	$38 - 42$
Frequency	$8$	$6$	$11$	$20$	$25$	$22$	$10$	$4$

Find the arithmetic mean of the following frequency distribution: Marked below 10 20 30 40 50 60 70 80 90 100 No. of students 12 22 35 50 70 86 97 104 109 115

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the arithmetic mean of the following frequency distribution:

Marked below $10$ $20$ $30$ $40$ $50$ $60$ $70$ $80$ $90$ $100$

No. of students $12$ $22$ $35$ $50$ $70$ $86$ $97$ $104$ $109$ $115$