From the table provided, let us calculate the requested values step-by-step.

Data Recap:

Intervals for SnapChat Messages:

• 0–4, 5–9, 10–14, 15–19, 20–24

Number of Teenagers in each Interval:

• 5, 8, 4, 9, 3

Step 1: Midpoints of Each Interval

To compute the mean and standard deviation, we'll calculate the midpoint of each class:

• 0–4: (0+4)/2 = 2
• 5–9: (5+9)/2 = 7
• 10–14: (10+14)/2 = 12
• 15–19: (15+19)/2 = 17
• 20–24: (20+24)/2 = 22

Step 2: Mean Calculation

The formula for the mean is:

$\text{Mean} = \frac{\sum (f \cdot x)}{\sum f}$

Where:

• $f$ = frequency (number of teenagers)
• $x$ = midpoint of the interval

$\text{Sum of } f \cdot x = (5 \cdot 2) + (8 \cdot 7) + (4 \cdot 12) + (9 \cdot 17) + (3 \cdot 22)$

Calculations: $(5 \cdot 2) = 10,\ (8 \cdot 7) = 56,\ (4 \cdot 12) = 48,\ (9 \cdot 17) = 153,\ (3 \cdot 22) = 66$

$\text{Sum of } f \cdot x = 10 + 56 + 48 + 153 + 66 = 333$

$\text{Sum of } f = 5 + 8 + 4 + 9 + 3 = 29$

$\text{Mean} = \frac{333}{29} \approx 11.48$

Step 3: Modal Class

The modal class is the class with the highest frequency. From the table:

• Frequency values: 5, 8, 4, 9, 3
• Highest frequency = 9 (class: 15–19)

Modal Class: 15–19

Step 4: Standard Deviation

The formula for the standard deviation is:

$\text{Standard Deviation} = \sqrt{\frac{\sum f \cdot (x - \text{Mean})^2}{\sum f}}$

We'll compute $f \cdot (x - \text{Mean})^2$:

$x - \text{Mean} = 2 - 11.48,\ 7 - 11.48,\ 12 - 11.48,\ 17 - 11.48,\ 22 - 11.48$

$x - \text{Mean} = -9.48,\ -4.48,\ 0.52,\ 5.52,\ 10.52$

Square each: $(-9.48)^2 = 89.90,\ (-4.48)^2 = 20.07,\ (0.52)^2 = 0.27,\ (5.52)^2 = 30.47,\ (10.52)^2 = 110.71$

Multiply by $f$: $f \cdot (x - \text{Mean})^2 = (5 \cdot 89.90), (8 \cdot 20.07), (4 \cdot 0.27), (9 \cdot 30.47), (3 \cdot 110.71)$

$(5 \cdot 89.90) = 449.5,\ (8 \cdot 20.07) = 160.56,\ (4 \cdot 0.27) = 1.08,\ (9 \cdot 30.47) = 274.23,\ (3 \cdot 110.71) = 332.13$

$\text{Sum of } f \cdot (x - \text{Mean})^2 = 449.5 + 160.56 + 1.08 + 274.23 + 332.13 = 1217.5$

Finally: $\text{Standard Deviation} = \sqrt{\frac{1217.5}{29}} \approx \sqrt{41.98} \approx 6.48$

Final Answers:

(a) Mean Number of Messages Sent: $11.48$
(b) Modal Class: $15–19$
(c) Standard Deviation: $6.48$

Would you like further clarifications or detailed steps? Here are some follow-up questions:

1. Can I explain the significance of standard deviation in this context?
2. Would you like a breakdown of how to handle grouped data in general?
3. Do you need help with similar statistical problems?
4. Would you like visual representations for mean and standard deviation?
5. Should I verify or expand on any specific calculations?

Tip: Always double-check midpoints and intervals when working with grouped data to avoid errors in calculations!