Question

The data represents the body mass index​ (BMI) values for $20$ females. Construct a frequency distribution beginning with a lower class limit of $15.0$ and use a class width of $6.0$. Does the frequency distribution appear to be roughly a normal​ distribution?

$$\begin{gathered} 17.7,29.4,19.2,27.5,33.5 \\ 25.6,22.1,44.9,26.5,18.3 \\ 22.4,32.4,24.9,28.6,37.7 \\ 26.1,21.8,21.2,30.7,21.4 \end{gathered}$$

Answer 1

Step 1: Calculating the number of classes formed

Finding the number of classes as $w=\frac{max-min}{n}$ where, $w$ is width is given to us $w=6$, maximum and minimum value from given data is,

$$\begin{gathered} max=44.9 \\ min=17.7 \end{gathered}$$

Therefore,

$$\begin{gathered} \Rightarrow 6=\frac{44.9-17.7}{n} \\ \Rightarrow n\approx 5 \end{gathered}$$

So, there will be a total of five classes with the lower value given to us $15.0$ and with a width of $6$

Step 2: Forming the table

S.No	Classes	Frequency of BMI
$1$	$15.0-20.9$	$3$
$2$	$21.0-26.9$	$9$
$3$	$27.0-32.9$	$5$
$4$	$33.0-38.9$	$2$
$5$	$39.0-44.9$	$1$

Step 3: Analyzing the kind of distribution

For a normal distribution, the frequency must increase to a maximum and then again come back to a lesser value. Also, it should be symmetric about the maximum value and here both conditions fail so this distribution is not normal.

Hence, the frequency distribution has been constructed and the distribution is roughly not normal.