Studdy AI Logo
Math

QuestionCalculate the sample variance for 'Living Area' of 'Commercial' buildings: {318, 3630, 59506, 3780, 22817}. Round to whole number.

Studdy Solution

STEP 1

Assumptions1. The data for 'Living Area' of 'Commercial' buildings is \{318,3630,59506,3780,22817\}. . We are asked to find the sample variance of this data.
3. The sample variance is calculated using the formulas^ = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^where s^ is the sample variance, nn is the number of observations, xix_i is each individual observation, and xˉ\bar{x} is the mean of the observations.

STEP 2

First, we need to find the mean of the data. The mean is calculated as the sum of all observations divided by the number of observations.
xˉ=1n∑i=1nxi\bar{x} = \frac{1}{n} \sum_{i=1}^{n} x_i

STEP 3

Plug in the given values for the observations to calculate the mean.
xˉ=15(318+3630+59506+3780+22817)\bar{x} = \frac{1}{5} (318 +3630 +59506 +3780 +22817)

STEP 4

Calculate the mean.
xˉ=1(318+3630+59506+3780+22817)=18110.2\bar{x} = \frac{1}{} (318 +3630 +59506 +3780 +22817) =18110.2

STEP 5

Now that we have the mean, we can calculate the sample variance. First, we need to find the sum of the squared differences between each observation and the mean.
∑i=1n(xi−xˉ)2=(318−18110.2)2+(3630−18110.2)2+(59506−18110.2)2+(3780−18110.2)2+(22817−18110.2)2\sum_{i=1}^{n} (x_i - \bar{x})^2 = (318 -18110.2)^2 + (3630 -18110.2)^2 + (59506 -18110.2)^2 + (3780 -18110.2)^2 + (22817 -18110.2)^2

STEP 6

Calculate the sum of the squared differences.
∑i=1n(xi−xˉ)2=(318−18110.2)2+(3630−18110.2)2+(59506−18110.2)2+(3780−18110.2)2+(22817−18110.2)2=4.085×109\sum_{i=1}^{n} (x_i - \bar{x})^2 = (318 -18110.2)^2 + (3630 -18110.2)^2 + (59506 -18110.2)^2 + (3780 -18110.2)^2 + (22817 -18110.2)^2 =4.085 \times10^9

STEP 7

Now we can calculate the sample variance using the formula.
s2=1n−1∑i=1n(xi−xˉ)2s^2 = \frac{1}{n-1} \sum_{i=1}^{n} (x_i - \bar{x})^2

STEP 8

Plug in the values for the number of observations and the sum of the squared differences to calculate the sample variance.
s^2 = \frac{1}{5-1} \times4.085 \times10^

STEP 9

Calculate the sample variance.
s2=4×4.085×9=.021×9s^2 = \frac{}{4} \times4.085 \times^9 =.021 \times^9

STEP 10

Finally, we need to round the sample variance to the nearest whole number.
s2=round(.021×109)s^2 = \text{round}(.021 \times10^9)

STEP 11

Calculate the rounded sample variance.
s=round(.021×109)=1021000000s^ = \text{round}(.021 \times10^9) =1021000000The sample variance for the 'Living Area' of 'Commercial' buildings is,021,000,000.

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord