Let's go step by step to construct a frequency distribution using 5 classes and 50 as the first lower class limit for the given exam scores:

Step 1: Identify the Range

First, we calculate the range of the dataLet's go step by step to construct a frequency distribution using 5 classes and 50 as the first lower class limit for the given exam scores:

Step 1: Identify the Range

First, we calculate the range of the

• Minimum score = 51
• Maximum score = 99
• Range = Maximum - Minimum = 99 - 51 = 48

Step 2: Determine Class Width

Next, we calculate the class width by dividing the range by the number of classes (which is 5):

• Class width = $\frac{48}{5} = 9.6$
  • We round up to the nearest whole number, so the class width becomes 10.

Step 3: Set Class Limits

We start with 50 as the first lower class limit. Using the class width of 10, the class limits will be:

1. 50 - 59
2. 60 - 69
3. 70 - 79
4. 80 - 89
5. 90 - 99

Step 4: Tally the Data

Now, we tally the number of data points in each class.

Class Interval	Tally	Frequency
50 - 59	51	1
60 - 69	63, 67, 67, 68, 69, 69	6
70 - 79	70, 70, 72, 73, 74, 75, 75, 78, 78	9
80 - 89	80, 81, 83, 85, 88, 89, 89	7
90 - 99	94, 99	2

Step 5: Construct the Frequency Distribution Table

Class Interval	Frequency
50 - 59	1
60 - 69	6
70 - 79	9
80 - 89	7
90 - 99	2

This is the frequency distribution for the given data.

Would you like more details on this, or any clarification?

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Here are 5 related questions to deepen understanding:

1. How would you calculate relative frequency for each class?
2. What is the cumulative frequency distribution for this data?
3. How would you create a histogram based on this frequency distribution?
4. How does changing the number of classes affect the frequency distribution?
5. How do you interpret skewness in the frequency distribution?

Tip: When determining class width, always round up the calculated width to ensure all data is included in the intervals.