The data below reps the ages in months at which 6 most babies started walking: 9, 11, 12, 13, 11 and 10…

Question

The data below reps the ages in months at which 6 most babies started walking: 9, 11, 12, 13, 11 and 10. Without using a calculator, find the exact value of the variance of the data.

ScanSolve AI Tutor · Accepted Answer

Haya Pretty, hapa kuna suluhisho la swali lako la takwimu:

Swali: Data iliyo hapa chini inawakilisha umri katika miezi ambapo watoto 6 walianza kutembea: $9, 11, 12, 13, 11$ na 10. Bila kutumia kikokotoo, pata thamani kamili ya variance ya data.

Panga data na ukokotoe wastani (mean), $\bar{x}$ .
Data iliyopangwa: $9, 10, 11, 11, 12, 13$ .
Jumla ya data, $\sum x = 9 + 10 + 11 + 11 + 12 + 13 = 66$ .
Idadi ya data, $n = 6$ .
Wastani, $\bar{x} = \frac{\sum x}{n} = \frac{66}{6} = 11$ .

Jaza jedwali kwa kukokotoa $x - \bar{x}$ na $(x - \bar{x})^2$ kwa kila thamani ya $x$ .

ages ( $x$ )	$x - \bar{x}$	$(x - \bar{x})^2$
9	$9 - 11 = -2$	$(-2)^2 = 4$
10	$10 - 11 = -1$	$(-1)^2 = 1$
11	$11 - 11 = 0$	$(0)^2 = 0$
11	$11 - 11 = 0$	$(0)^2 = 0$
12	$12 - 11 = 1$	$(1)^2 = 1$
13	$13 - 11 = 2$	$(2)^2 = 4$

Kokotoa jumla ya $(x - \bar{x})^2$ .
$\sum (x - \bar{x})^2 = 4 + 1 + 0 + 0 + 1 + 4 = 10$
Kokotoa variance ( $\sigma^2$ ).
Fomula ya variance ni $\sigma^2 = \frac{\sum (x - \bar{x})^2}{n}$ .
$\sigma^2 = \frac{10}{6}$ $\sigma^2 = \frac{5}{3}$
Thamani kamili ya variance ya data ni $\boxed{\mathbf{\frac{5}{3}}}$ .

Hiyo ni yote kwa leo! Umefanya vizuri sana.

The data below reps the ages in months at which 6 most babies started walking: 9, 11, 12, 13, 11 and 10. Without using a calculator, find the exact value of the variance of the data.

Answer

Step-by-step solution

Panga data na ukokotoe wastani (mean), $\bar{x}$ .

Jaza jedwali kwa kukokotoa $x - \bar{x}$ na $(x - \bar{x})^2$ kwa kila thamani ya $x$ .

Kokotoa jumla ya $(x - \bar{x})^2$ .

Kokotoa variance ( $\sigma^2$ ).

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The data below reps the ages in months at which 6 most babies started walking: 9, 11, 12, 13, 11 and 10. Without using a calculator, find the exact value of the variance of the data.

Answer

Step-by-step solution

Panga data na ukokotoe wastani (mean), xˉ\bar{x}xˉ.

Jaza jedwali kwa kukokotoa x−xˉx - \bar{x}x−xˉ na (x−xˉ)2(x - \bar{x})^2(x−xˉ)2 kwa kila thamani ya xxx.

Kokotoa jumla ya (x−xˉ)2(x - \bar{x})^2(x−xˉ)2.

Kokotoa variance (σ2\sigma^2σ2).

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Still stuck on this one?

More Mathematics Questions

Panga data na ukokotoe wastani (mean), $\bar{x}$ .

Jaza jedwali kwa kukokotoa $x - \bar{x}$ na $(x - \bar{x})^2$ kwa kila thamani ya $x$ .

Kokotoa jumla ya $(x - \bar{x})^2$ .

Kokotoa variance ( $\sigma^2$ ).