Question

10 of the 6 years old kids were selected from a school and the height of each individual were shown as in the table

Individual Height (cm)

A 120.6

B 116.4

C 117.2

D 118.1

E 114.1

G 116.9

H 113.3

I 121.1

J 116.9

K 117.0

According to the national statistics report, the average height of 6 years old kids in the country is 120.0 cm. What is the T score of this sample？

Answer 1

$$mean=\bar{x}=\dfrac{1}{10}(120.6+116.4+117.2$$

$$+118.1+114.1+116.9+113.3$$

$$+121.1+116.9+117.0)=117.16$$

$$s^2=\dfrac{\sum_i(x_i-\bar{x})^2}{n-1}$$

$$=\dfrac{1}{10-1}((120.6-117.16)^2+(116.4-117.16)^2$$

$$+(117.2-117.16)^2+(118.1-117.16)^2$$

$$+(114.1-117.16)^2+(116.9-117.16)^2$$

$$+(113.3-117.16)^2+(121.1-117.16)^2$$

$$+(116.9-117.16)^2+(117.0-117.16)^2)$$

$$=\dfrac{53.244}{9}=5.916$$

$$t=\dfrac{\bar{x}-\mu}{s/\sqrt{n}}=\dfrac{117.16-120.0}{\sqrt{5.916}/\sqrt{10}}$$

$$\approx-3.692362$$