Question

cortnis teacher has accused them of being out on passes too much! heres the data (in minutes): 27, 9, 7, 10, 10, 17, 14, 15, 14, 10, 10, 18, 12, 15. make a box - plot of these data.
mean
st. dev
min
q1
median
q3
max

Explanation:

Step1: Organize data in ascending order

7, 10, 10, 10, 12, 14, 14, 15, 15, 17, 18, 27

Step2: Calculate the mean

$\text{Mean}=\frac{7 + 10+10+10+12+14+14+15+15+17+18+27}{12}=\frac{179}{12}\approx14.92$

Step3: Calculate the standard - deviation

First, find the variance.

1. Calculate the deviation of each data point from the mean:

$(7 - 14.92)^2,(10 - 14.92)^2,(10 - 14.92)^2,(10 - 14.92)^2,(12 - 14.92)^2,(14 - 14.92)^2,(14 - 14.92)^2,(15 - 14.92)^2,(15 - 14.92)^2,(17 - 14.92)^2,(18 - 14.92)^2,(27 - 14.92)^2$

1. Find the average of the squared - deviations (variance).

$\text{Variance}=\frac{(7 - 14.92)^2+(10 - 14.92)^2+(10 - 14.92)^2+(10 - 14.92)^2+(12 - 14.92)^2+(14 - 14.92)^2+(14 - 14.92)^2+(15 - 14.92)^2+(15 - 14.92)^2+(17 - 14.92)^2+(18 - 14.92)^2+(27 - 14.92)^2}{12}$
$=\frac{62.7264 + 24.2064+24.2064+24.2064 + 8.5264+0.8464+0.8464+0.0064+0.0064+4.3264+9.4864+145.9264}{12}$
$=\frac{304.3168}{12}\approx25.36$
$\text{St. Dev}=\sqrt{25.36}\approx5.04$

Step4: Find the minimum value

The minimum value is 7.

Step5: Find the first quartile (Q1)

The lower half of the data is 7, 10, 10, 10, 12, 14. The median of the lower half is $\frac{10 + 10}{2}=10$.

Step6: Find the median

Since $n = 12$ (even), the median is $\frac{14+14}{2}=14$.

Step7: Find the third quartile (Q3)

The upper half of the data is 15, 15, 17, 18, 27. The median of the upper half is $\frac{15 + 17}{2}=16$.

Step8: Find the maximum value

The maximum value is 27.

Answer:

Statistic	Value
St. Dev	$\approx5.04$
Min	7
Q1	10
Median	14
Q3	16
Max	27