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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].
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