1. Given data

The values are: $x_i: 0,1,5,6,10,12,17$ with corresponding frequencies $f_i: 3,2,3,2,6,3,3$

We use the variance formula for a frequency distribution: $\sigma^2=\frac{\sum f_i(x_i-\bar{x})^2}{\sum f_i}$ where $\bar{x}=\frac{\sum f_ix_i}{\sum f_i}$

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2. Find total frequency

$N=\sum f_i=3+2+3+2+6+3+3=22$

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3. Find the mean

Compute $\sum f_i x_i$:

$\sum f_i x_i=3(0)+2(1)+3(5)+2(6)+6(10)+3(12)+3(17)$

$=0+2+15+12+60+36+51=176$

Hence, $\bar{x}=\frac{176}{22}=8$

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4. Compute $\sum f_i (x_i-\bar{x})^2$

Since $\bar{x}=8$,

$\sum f_i(x_i-8)^2$

Now calculate term by term:

• For $x=0$, $f=3$: $3(0-8)^2=3(64)=192$
• For $x=1$, $f=2$: $2(1-8)^2=2(49)=98$
• For $x=5$, $f=3$: $3(5-8)^2=3(9)=27$
• For $x=6$, $f=2$: $2(6-8)^2=2(4)=8$
• For $x=10$, $f=6$: $6(10-8)^2=6(4)=24$
• For $x=12$, $f=3$: $3(12-8)^2=3(16)=48$
• For $x=17$, $f=3$: $3(17-8)^2=3(81)=243$

Adding: $192+98+27+8+24+48+243=640$

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5. Find the variance

$\sigma^2=\frac{640}{22}=\frac{320}{11}\approx 29.09$

Since this is an integer-type question, the exact variance is: $\boxed{\frac{320}{11}}$

If the question expects the nearest integer, it is $29$.

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6. Compare with stored answer

Stored correct answer: $29$

Our computed variance is $\sigma^2=\frac{320}{11}\approx 29.09$ So the exact answer is not exactly $29$, but its approximate value is $29$.

Therefore, I do not fully agree with the stored answer if exact variance is required.