Question

a sample of 20 participants took part in a hearing experiment. among other things, the absolute hearing threshold (in decibels) was measured for each participant. the 20 measurements were as follows: 25, 22, 18, 35, 37, 34, 31, 27, 24, 21, 18, 39, 23, 23, 20, 20, 20, 17, 17, 32 send data to calculator draw the histogram for these data using an initial class boundary of 16.5, an ending class boundary of 41.5, and 5 classes of equal width. note that you or remove classes from the figure. label each class with its endpoints.

Explanation:

Step1: Calculate class - width

The formula for class - width $w=\frac{\text{ending boundary}-\text{initial boundary}}{\text{number of classes}}$. Here, the initial class boundary is $16.5$, the ending class boundary is $41.5$, and the number of classes is $5$. So, $w=\frac{41.5 - 16.5}{5}=\frac{25}{5}=5$.

Step2: Determine class intervals

The first class has a lower - limit of $16.5$. The class intervals are:
Class 1: $16.5 - 21.5$
Class 2: $21.5 - 26.5$
Class 3: $26.5 - 31.5$
Class 4: $31.5 - 36.5$
Class 5: $36.5 - 41.5$

Step3: Count frequencies

For the class $16.5 - 21.5$: The data values in this range are $18,18,21,20,20,20,17,17$, so the frequency is $8$.
For the class $21.5 - 26.5$: The data values are $25,22,24,23,23$, so the frequency is $5$.
For the class $26.5 - 31.5$: The data values are $31,27$, so the frequency is $2$.
For the class $31.5 - 36.5$: The data values are $35,34,32$, so the frequency is $3$.
For the class $36.5 - 41.5$: The data values are $37,39$, so the frequency is $2$.

Step4: Draw the histogram

On the x - axis, label the class intervals with their endpoints ($16.5,21.5,26.5,31.5,36.5,41.5$). On the y - axis, label the frequencies from $0$ to $8$. Draw rectangles for each class with heights corresponding to their frequencies.

Answer:

The class intervals and their frequencies are:
$16.5 - 21.5$: Frequency $8$
$21.5 - 26.5$: Frequency $5$
$26.5 - 31.5$: Frequency $2$
$31.5 - 36.5$: Frequency $3$
$36.5 - 41.5$: Frequency $2$