Question

② high temperature frequency 78 4 82 3 85 2 98 3 101 1 mean = median = mode =

Explanation:

Step1: Calculate Total Frequency

Sum the frequencies: \( 4 + 3 + 2 + 3 + 1 = 13 \)

Step2: Calculate Mean

Multiply each temperature by its frequency, sum them, then divide by total frequency.
\( (78\times4)+(82\times3)+(85\times2)+(98\times3)+(101\times1) = 312 + 246 + 170 + 294 + 101 = 1123 \)
Mean: \( \frac{1123}{13} \approx 86.38 \)

Step3: Find Median

Total frequency \( n = 13 \) (odd). The median is the \( \frac{n + 1}{2} = 7 \)-th term.
Cumulative frequencies:

• 78: 4 (cumulative: 4)
• 82: 3 (cumulative: \( 4 + 3 = 7 \))

So the 7th term is 82. Median = 82.

Step4: Find Mode

The temperature with the highest frequency. 78 has frequency 4 (highest). Mode = 78.

Answer:

Mean: \( \approx 86.38 \), Median: \( 82 \), Mode: \( 78 \)