Name: Measures of Central Tendency
Uploaded: 2019-07-19
Duration: 11 min 23 s
Description: There are three main measures of central tendency: the mode, the median, and the mean. Each of these measures describes a different indication. Learn more.

Question

Find the mean and variance of the following data by using step deviation method:

Classes	$0 - 5$	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency	$20$	$24$	$32$	$28$	$20$	$11$	$26$	$15$	$24$

Accepted Answer

Classes Class Mark $0 - 5$ $5 - 10$ $d_{i} = x_{i} - A A = 22.5$ $u_{i} = \frac{d_{i}}{C} C = 5$ $40 - 45$ $f_{i} {u_{i}}^{2}$

$0 - 5$ $2.5$ $- 20$ $- 4$ $- 80$ $320$

$5 - 10$ $7.5$ $24$ $- 15$ $- 3$ $- 72$ $216$

$10 - 15$ $12.5$ $32$ $- 10$ $- 2$ $- 64$ $128$

$15 - 20$ $17.5$ $28$ $- 5$ $20$ $- 28$ $28$

$20 - 25$ $22.5$ $20$ $- 0$ $0$ $0$ $0$

$25 - 30$ $27.5$ $11$ $5$ $1$ $11$ $11$

$30 - 35$ $32.5$ $26$ $10$ $2$ $52$ $104$

$35 - 40$ $37.5$ $15$ $15$ $3$ $45$ $135$

$40 - 45$ $42.5$ $24$ $20$ $4$ $96$ $384$

$Σ f_{i} = 200$ $Σ f_{i} u_{i} = - 40$ $Σ f_{i} {u_{i}}^{2} = 1326$

By step deviation method, mean $= A + \frac{Σ f_{i} u_{i}}{Σ f_{i}} \times C$

$= 22 .5 - \frac{40}{200} \times 5$

$= 22 .5 - 1$

$= 21 .5$

And, $S.D (σ) = \sqrt{\frac{\sum f_{i} u_{i}^{2}}{Σ f_{i}} - {(\frac{Σ f_{i} u_{i}}{Σ f_{i}})}^{2}} \times C$

$= \sqrt{\frac{1326}{200} - {(\frac{- 40}{200})}^{2}} \times 5$

$= \sqrt{6 .63 - 0 .04} \times 5$

$= 12 .83549$

So, variance, $σ^{2} = 164 .75$

Height (in $cm$ )	$70 - 75$	$75 - 80$	$80 - 85$	$85 - 90$	$52$	$95 - 100$	$100 - 105$	$105 - 110$	$15$
Number of children	$135$	$4$	$7$	$7$	$15$	$9$	$6$	$6$	$3$

Variables	$10 - 20$	$20 - 30$	$30 - 40$	$40 - 50$	$50 - 60$	$60 - 70$
Series $A$	$10$	$16$	$30$	$40$	$26$	$18$
Series $B$	$22$	$18$	$32$	$34$	$18$	$16$

Find the mean and variance of the following data by using step deviation method:

Classes $0 - 5$ $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$

Frequency $20$ $24$ $32$ $28$ $20$ $11$ $26$ $15$ $24$

Important Questions on Statistics

Learn and Prepare for any exam you want !

Mid-point	$5$	$15$	$Σ f_{i} {u_{i}}^{2} = 1326$	$35$	$45$	$55$	$65$	$75$
Frequency	$5$	$8$	$7$	$12$	$28$	$= 22 .5 - \frac{40}{200} \times 5$	$10$	$10$

Find the mean and variance of the following data by using step deviation method: Classes 0-5 5-10 10-15 15-20 20-25 25-30 30-35 35-40 40-45 Frequency 20 24 32 28 20 11 26 15 24

Important Questions on Statistics

Learn and Prepare for any exam you want !

Find the mean and variance of the following data by using step deviation method:

Classes $0 - 5$ $5 - 10$ $10 - 15$ $15 - 20$ $20 - 25$ $25 - 30$ $30 - 35$ $35 - 40$ $40 - 45$

Frequency $20$ $24$ $32$ $28$ $20$ $11$ $26$ $15$ $24$