Question

1.46/47 means, medians, standard deviations, and iqrs: answer the following about each dataset. (round to two decimal places where appropriate) dataset i: 1 2 3 4 5 a) the median of dataset i is: b) the iqr of dataset i is from to c) the mean of dataset i is: d) the standard deviation of dataset i is: dataset ii: 6 7 8 9 10 e) the median of dataset ii is: f) the iqr of dataset ii is from to g) the mean of dataset ii is: h) the standard deviation of dataset ii is: question help: video submit all parts

Explanation:

Step1: Calculate median of Dataset I

Dataset I is 1, 2, 3, 4, 5. Since there are 5 (odd - numbered) data points, the median is the middle - value. So the median is 3.

Step2: Calculate IQR of Dataset I

First, find the first quartile ($Q_1$) and third quartile ($Q_3$). For Dataset I, the lower half is 1, 2. So $Q_1=\frac{1 + 2}{2}=1.5$. The upper half is 4, 5. So $Q_3=\frac{4+5}{2}=4.5$. The IQR is from 1.5 to 4.5.

Step3: Calculate mean of Dataset I

The mean $\bar{x}=\frac{1 + 2+3+4+5}{5}=\frac{15}{5}=3$.

Step4: Calculate standard deviation of Dataset I

The formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_i-\bar{x})^2}{n - 1}}$.
$\sum_{i=1}^{5}(x_i - 3)^2=(1 - 3)^2+(2 - 3)^2+(3 - 3)^2+(4 - 3)^2+(5 - 3)^2=4 + 1+0+1+4 = 10$.
$s=\sqrt{\frac{10}{4}}\approx1.58$.

Step5: Calculate median of Dataset II

Dataset II is 6, 7, 8, 9, 10. Since there are 5 (odd - numbered) data points, the median is 8.

Step6: Calculate IQR of Dataset II

The lower half is 6, 7. So $Q_1=\frac{6 + 7}{2}=6.5$. The upper half is 9, 10. So $Q_3=\frac{9+10}{2}=9.5$. The IQR is from 6.5 to 9.5.

Step7: Calculate mean of Dataset II

The mean $\bar{x}=\frac{6 + 7+8+9+10}{5}=\frac{40}{5}=8$.

Step8: Calculate standard deviation of Dataset II

$\sum_{i = 1}^{5}(x_i - 8)^2=(6 - 8)^2+(7 - 8)^2+(8 - 8)^2+(9 - 8)^2+(10 - 8)^2=4+1+0+1+4 = 10$.
$s=\sqrt{\frac{10}{4}}\approx1.58$.

Answer:

a) 3
b) 1.5, 4.5
c) 3
d) 1.58
e) 8
f) 6.5, 9.5
g) 8
h) 1.58