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**Topic**

The forecast results of the highest temperature for 10 consecutive days in Nghe An at the end of January 2022 are given in the following table:

Day |
22 |
23 |
24 |
25 |
26 |
27 |
28 |
29 |
30 |
thirty first |

Temperature (degrees Celsius) |
23 |
25 |
26 |
27 |
27 |
27 |
27 |
21 |
19 |
18 |

a) Write a sample of the temperature statistics obtained from the table above

b) Calculate the mean, variance, and standard deviation of that data sample

**Solution method – See details**

+ Write the data samples in non-increasing order

+ Use the formula to calculate the average: \(\overline x = \frac{{{x_1} + {x_2} + … + {x_n}}}{n}\)

+ Find the variance using the formula \({S^2} = \frac{1}{n}\left( {{n_1}{x_1}^2 + {n_2}{x_2}^2 + … + {n_k}) {x_k}^2} \right) – {\overline x ^2}\) and standard deviation \(S = \sqrt {{S^2}} \)

**Detailed explanation**

a) Write data samples in non-increasing order: 23; 25; 26; 27; 27; 27; 26; 21; 19; 18

b)

+ The mean of the data sample is: \(\overline x = \frac{{23 + 25 + 26 + 27 + 27 + 27 + 26 + 21 + 19 + 18}}{{10}} = 24\)

+ Variance: \({S^2} = \frac{1}{{10}}\left( {{{23}^2} + {{25}^2} + … + {{18}^2 ) }} \right) – {24^2} = 11,2\)

+ Standard Deviation: \(S = \sqrt {{S^2}} = \sqrt {11,2} = \frac{{2\sqrt {70} }}{5}\)

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