The image you uploaded contains a table showing temperature intervals and their corresponding frequencies, as well as questions related to the data.

Extracted Information:

• Temperature (°C):
  • $0 \leq T < 5$ : Frequency = 2
  • $5 \leq T < 10$ : Frequency = 4
  • $10 \leq T < 15$ : Frequency = 6
  • $15 \leq T < 20$ : Frequency = 7
  • $20 \leq T < 25$ : Frequency = 6
  • $25 \leq T < 30$ : Frequency = 5

The questions are:

1. Find the modal class interval.
2. Calculate an estimate for the mean temperature.

Solutions:

1. Finding the Modal Class Interval

The modal class interval is the class interval with the highest frequency. From the table, the highest frequency is 7, which corresponds to the interval $15 \leq T < 20$.

Modal class interval: $15 \leq T < 20$

2. Estimating the Mean Temperature

To estimate the mean temperature, we can use the midpoints of each class interval and apply the formula for the mean of grouped dataThe image you uploaded contains a table showing temperature intervals and their corresponding frequencies, as well as questions related to the data.

Extracted Information:

• Temperature (°C):
  • $0 \leq T < 5$ : Frequency = 2
  • $5 \leq T < 10$ : Frequency = 4
  • $10 \leq T < 15$ : Frequency = 6
  • $15 \leq T < 20$ : Frequency = 7
  • $20 \leq T < 25$ : Frequency = 6
  • $25 \leq T < 30$ : Frequency = 5

The questions are:

1. Find the modal class interval.
2. Calculate an estimate for the mean temperature.

Solutions:

1. Finding the Modal Class Interval

The modal class interval is the class interval with the highest frequency. From the table, the highest frequency is 7, which corresponds to the interval $15 \leq T < 20$.

Modal class interval: $15 \leq T < 20$

2. Estimating the Mean Temperature

To estimate the mean temperature, we can use the midpoints of each class interval and apply the formula for the mean of grouped

$\text{Estimated Mean} = \frac{\sum (\text{Midpoint} \times \text{Frequency})}{\sum \text{Frequency}}$

• Midpoints:

  • $0 \leq T < 5$ : Midpoint = 2.5
  • $5 \leq T < 10$ : Midpoint = 7.5
  • $10 \leq T < 15$ : Midpoint = 12.5
  • $15 \leq T < 20$ : Midpoint = 17.5
  • $20 \leq T < 25$ : Midpoint = 22.5
  • $25 \leq T < 30$ : Midpoint = 27.5

• Calculations:

  • $2.5 \times 2 = 5$
  • $7.5 \times 4 = 30$
  • $12.5 \times 6 = 75$
  • $17.5 \times 7 = 122.5$
  • $22.5 \times 6 = 135$
  • $27.5 \times 5 = 137.5$

$\text{Sum of Midpoint} \times \text{Frequency} = 5 + 30 + 75 + 122.5 + 135 + 137.5 = 505$

$\text{Sum of Frequencies} = 2 + 4 + 6 + 7 + 6 + 5 = 30$

$\text{Estimated Mean} = \frac{505}{30} \approx 16.83^\circ \text{C}$

Estimated Mean Temperature: $16.83^\circ \text{C}$

Would you like further details or explanations?

Follow-up Questions:

1. How is the median class interval calculated from grouped data?
2. What are the possible sources of error when estimating the mean from grouped data?
3. How does the range of the data set influence the spread of temperatures?
4. What is the significance of the mode in this data set, and how might it be used?
5. If the temperature intervals were smaller, how would that affect the mean estimate?

Tip: When estimating the mean from grouped data, remember that smaller class intervals can lead to a more accurate estimate.