question 24
answer to two decimal places
find the mode:
find the range:
find the standard deviation:
question help: video
submit question

Question

Accepted Answer

# Answer:
19, 26, 6.97

# Explanation:
## Step1: Find the mode
The mode is the number that appears most frequently. In the data set $18, 13, 19, 12, 27, 11, 15, 25, 19, 1$, the number $19$ appears twice and all other numbers appear only once.

## Step2: Find the range
The range is calculated as $ \text{Range}=\text{Max}-\text{Min}$. The maximum value in the data set is $27$ and the minimum value is $1$. So, $ \text{Range}=27 - 1=26$

## Step3: Find the standard deviation
First, find the mean $\bar{x}$.
$$
\bar{x}=\frac{18 + 13+19+12+27+11+15+25+19+1}{10}=\frac{150}{10} = 15
$$
Then, use the formula for the sample standard deviation $s=\sqrt{\frac{\sum_{i = 1}^{n}(x_{i}-\bar{x})^{2}}{n - 1}}$
$$
\begin{align*}
\sum_{i=1}^{10}(x_{i}-\bar{x})^{2}&=(18 - 15)^{2}+(13-15)^{2}+(19 - 15)^{2}+(12-15)^{2}+(27-15)^{2}+(11 - 15)^{2}+(15-15)^{2}+(25-15)^{2}+(19-15)^{2}+(1 - 15)^{2}\
&=9+4 + 16+9+144+16+0+100+16+196\
&=510
\end{align*}
$$
$$
s=\sqrt{\frac{510}{9}}\approx\sqrt{56.67}\approx6.97
$$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Find the mode

Step2: Find the range

Step3: Find the standard deviation

Answer: