Question

I don’t have a graphic calculator and I really need this information! :( I need a histogram of the next numbers: (specifically I need to know the shape, median, standard deviation, q1, q3)2 3 4 4 5 5 4 3 3 9 2 3 4 4 5 6 6 7 8 93 4 4 5 5 6 6 7 7 10

Answer 1

Check below, please

1) Let's find the median of this Data Set. Let's write them orderly so that we can get the median:

`\begin{gathered} 2,\: 2,\: 3,\: 3,\: 3,\: 3,\: 3,\: 4,\: 4,\: 4,\: 4,\: 4,\: 4,\: 4,\: 5,\: 5,\: 5,\: 5,\: 5,\: 6,\: 6,\: 6,\: 6,\: 7,\: 7,\: 7,\: 8,\: 9,\: 9,\: 10 \\ Md=(15th+16th)/(2)=(5+5)/(2)=5 \end{gathered}`

Note that the median from a Data Set with an even number of data points is the average between the middle number and the subsequent one.

2) Let's proceed to find the Standard Deviation:

`\begin{gathered} \sigma\mleft(X\mright)=\sqrt{\frac{\sum_(i=1)^n\left(x_i-\bar{x}\right)^2}{n-1}} \\ \sigma\mleft(X\mright)=\sqrt[]{4.36896} \\ \sigma\mleft(X\mright)=2.0902 \end{gathered}`

The Standard deviation is the square root of the variance of that distribution.

2.2) Let's proceed with the quartiles (q1, and q3):

`\begin{gathered} Q_1=4 \\ Q_3=6 \end{gathered}`

Calculating Q1 as the median of the 1st half of the distribution and Q3, as the median of the 2nd half of this distribution.

3) So based on that we have the following Histogram:

We can see that this Histogram is skewed to the right.