Let's work through the problem step by step, starting with constructing the frequency table.

1. Frequency Table

We have a set of intervals and the corresponding number of guesses within each interval.

Intervals (grams)	Frequency
0 - 9	4
10 - 19	5
20 - 29	9
30 - 39	14
40 - 49	12
50 - 59	4
60 - 69	2

2. Cumulative Frequency Table

Next, we calculate the cumulative frequency.

Intervals (grams)	Frequency	Cumulative Frequency
0 - 9	4	4
10 - 19	5	9
20 - 29	9	18
30 - 39	14	32
40 - 49	12	44
50 - 59	4	48
60 - 69	2	50

3. Cumulative Frequency Curve (Ogive)

To draw the cumulative frequency curve, plot the cumulative frequency against the upper boundary of each interval.

4. Estimations

a) Median Mass

The median is the value corresponding to the cumulative frequency of 25 (since $\frac{50}{2} = 25$).

• Step 1: Find the interval containing the 25th value.
• The cumulative frequency of 18 occurs at the interval 20-29, and the next interval (30-39) contains the 25th value.
• Step 2: Interpolate within the 30-39 interval to find the exact median.

Let's calculate this in more detail.

b) Interquartile Range

The interquartile range (IQR) is the difference between the upper quartile (Q3) and the lower quartile (Q1).

• Q1: The first quartile is at the 12.5th value. We'll interpolate to find this.
• Q3: The third quartile is at the 37.5th value. We'll interpolate to find this as well.

c) Number of People within 10 Grams of the Median

Once we have the median, we'll count how many guesses are within 10 grams of that value.

Frequency Curve

For the frequency curve, we can plot the midpoints of each interval against their frequencies and then draw a smooth curve.

Detailed Calculations

Let's go through the calculations for the median and interquartile range in detail.

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Would you like to proceed with the detailed calculations for the median, interquartile range, and the number of people within 10 grams of the median? Additionally, I can plot the cumulative frequency curve for better visualization.