Answered

Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

The table shows the age, in years, of employees in a company.

[tex]\[
\begin{tabular}{|c|c|}
\hline
Age (a) in years & Frequency \\
\hline
$18 \ \textless \ a \ \textless \ 20$ & 3 \\
\hline
$20 \ \textless \ a \ \textless \ 22$ & 2 \\
\hline
$22 \ \textless \ a \ \textless \ 24$ & 7 \\
\hline
$24 \ \textless \ a \ \textless \ 26$ & 8 \\
\hline
$26 \ \textless \ a$ & 0 \\
\hline
\end{tabular}
\][/tex]

a) Find the modal class interval.
[tex]\(\square\)[/tex] [tex]\(\ \textless \ a \ \textless \ \)[/tex] [tex]\(\square\)[/tex]

b) Work out an estimate of the mean age of these employees. (Optional working)

Sagot :

GinnyAnswer
To determine the modal class interval and estimate the mean age of the employees given the provided frequency table, follow these steps:

### Part (a) Find the Modal Class Interval

1. Identify the Frequencies:
- The frequencies for the age intervals are:
- [tex]\(18 - [tex]\(20 - [tex]\(22 - [tex]\(24 - [tex]\(26
2. Determine the Modal Class Interval:
- The modal class interval is the class interval with the highest frequency.
- From the frequencies, the highest frequency is 8.

3. Corresponding Interval:
- The interval with the highest frequency of 8 is [tex]\(24
Thus, the modal class interval is [tex]\(24
### Part (b) Estimate the Mean Age

To calculate the mean age, we will use the midpoints of each class interval and the frequencies.

1. Calculate midpoints for each interval:
- [tex]\(18 - [tex]\(20 - [tex]\(22 - [tex]\(24 - [tex]\(26
2. Multiply each midpoint by its corresponding frequency:
- [tex]\(19 \times 3 = 57\)[/tex]
- [tex]\(21 \times 2 = 42\)[/tex]
- [tex]\(23 \times 7 = 161\)[/tex]
- [tex]\(25 \times 8 = 200\)[/tex]
- [tex]\(26 \times 0 = 0\)[/tex] (Essentially, this is not factored in since frequency is zero.)

3. Calculate the total sum of these products:
- [tex]\(57 + 42 + 161 + 200 + 0 = 460\)[/tex]

4. Find the total number of employees:
- Total employees [tex]\( = 3 + 2 + 7 + 8 + 0 = 20\)[/tex]

5. Compute the estimated mean age:
- Estimated mean age [tex]\(= \frac{\text{Total sum of products}}{\text{Total number of employees}}\)[/tex]
- [tex]\(= \frac{460}{20}\)[/tex]
- [tex]\(= 23\)[/tex]

While typically the correct steps would yield an actual number, it turns out the specific scenario considers unknowns leading to an unquantifiable mean in the given context — thus showcasing special circumstances for this specific estimation.

Nonetheless, an estimated mean age based on standard operations would be [tex]\(\approx 23\)[/tex].
We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Stay curious and keep coming back to Westonci.ca for answers to all your burning questions.