Math  /  Data & Statistics

QuestionFor 76 employees of a large department store, the distribution shown here for years of service was obtained, Draw a histogram and frequency polygon for th data. \begin{tabular}{lc} Class & Frequency \\ \hline 151-5 & 25 \\ 6106-10 & 24 \\ 111511-15 & 14 \\ 162016-20 & 2 \\ 212521-25 & 8 \\ 263026-30 & 3 \\ \hline \end{tabular}
Part: 0/20 / 2
Part 1 of 2
Draw a frequency histogram. Years of Service for Employees in a Department Store
Fint: 1 / 2 Part 2 of 2 Drew a twจมuency palygon.

Studdy Solution

STEP 1

What is this asking? We need to visually represent the years of service for employees using a histogram and a frequency polygon. Watch out! Make sure the bars in the histogram touch each other and the polygon connects the midpoints of the bars.

STEP 2

1. Prepare the data
2. Draw the histogram
3. Draw the frequency polygon

STEP 3

To draw the frequency polygon later, we'll need the midpoint of each class interval.
Let's calculate those now!
For the interval 11-55, the midpoint is 1+52=62=3\frac{1+5}{2} = \frac{6}{2} = 3.
Similarly, for 66-1010, it's 6+102=162=8\frac{6+10}{2} = \frac{16}{2} = 8.
Continuing this, we get midpoints **3, 8, 13, 18, 23,** and **28**.

STEP 4

We'll have the "Years of Service" on the horizontal x-axis and "Frequency" on the vertical y-axis.

STEP 5

For the interval 11-55, the frequency is **25**, so we draw a bar from 11 to 55 with a height of 2525.
Next, for 66-1010, the frequency is **24**, so the bar goes from 66 to 1010 with a height of 2424.
We continue this for all the intervals, making sure the bars touch each other.

STEP 6

Using the midpoints we calculated earlier, we plot a point above each midpoint at the height matching its frequency.
So, above midpoint **3**, we plot a point at a height of **25** (the frequency).
Above midpoint **8**, we plot a point at **24**, and so on.

STEP 7

Now, connect these points with straight lines.
To complete the polygon, extend the lines at each end down to the x-axis.
On the left side, extend the line from the first point (above **3**) down to zero frequency at the beginning of the previous interval (which would be zero).
On the right side, extend the line from the last point (above **28**) down to zero frequency at the end of the next interval (which would be 31).
This creates a closed polygon!

STEP 8

The histogram has bars representing the frequency of each range of years of service, touching each other.
The frequency polygon is overlaid, connecting the midpoints of each bar's top with straight lines, and extending down to the x-axis at zero frequency on both ends.

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