Question

listed below are the average wedding cost (in thousands) of 20 randomly selected newly wed couples in 2019.
22 23 23 23 25 26 26 27 27 27
27 27 28 29 30 30 33 33 33 35

a) find the class width to construct a frequency distribution table using 4 classes.
the class width is

b) use the class width from part a to construct the table.

classes	frequency
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Explanation:

Part (a)

Step 1: Find the range

First, we find the range of the data. The range is the maximum value minus the minimum value. The minimum value in the data set is 22 and the maximum value is 35. So, the range \( R = 35 - 22 = 13 \).

Step 2: Calculate the class width

To find the class width when we have \( k \) classes, we use the formula \( \text{Class Width} = \frac{\text{Range}}{\text{Number of Classes}} \). Here, the number of classes \( k = 4 \) and the range \( R = 13 \). So, \( \text{Class Width} = \frac{13}{4} = 3.25 \). But we usually round up to the next whole number to ensure all data points are covered. So, the class width is 4.

Step 1: Determine class intervals

Using the class width of 4, start from the minimum value (22) to form intervals: \( 22 - 25 \), \( 26 - 29 \), \( 30 - 33 \), \( 34 - 37 \).

Step 2: Count frequencies

Count how many data points fall into each interval:

• \( 22 - 25 \): 5 data points.
• \( 26 - 29 \): 9 data points.
• \( 30 - 33 \): 5 data points.
• \( 34 - 37 \): 1 data point.

Answer:

4

Part (b)

First, we determine the class intervals using the class width of 4. The first class starts at the minimum value, 22.

• First class: \( 22 - 25 \) (since \( 22 + 4 - 1 = 25 \))
• Second class: \( 26 - 29 \) ( \( 26 = 22 + 4 \), \( 29 = 26 + 4 - 1 \))
• Third class: \( 30 - 33 \) ( \( 30 = 26 + 4 \), \( 33 = 30 + 4 - 1 \))
• Fourth class: \( 34 - 37 \) ( \( 34 = 30 + 4 \), \( 37 = 34 + 4 - 1 \))

Now, we count the frequency of each class:

• For class \( 22 - 25 \): The data points are 22, 23, 23, 23, 25. So, frequency \( = 5 \).
• For class \( 26 - 29 \): The data points are 26, 26, 27, 27, 27, 27, 27, 28, 29. So, frequency \( = 9 \).
• For class \( 30 - 33 \): The data points are 30, 30, 33, 33, 33. So, frequency \( = 5 \).
• For class \( 34 - 37 \): The data point is 35. So, frequency \( = 1 \).