Question

which data set has a mean of 66, a median of 66, and a mode of 83?
85, 19, 62, 84, 93, 62, 63, 83, 77, 89, 43
60, 33, 55, 68, 64, 82, 78, 12, 39, 39, 40
79, 29, 72, 54, 83, 57, 63, 83, 75, 66, 65
55, 38, 44, 39, 30, 55, 58, 68, 72, 78, 28
question #6
the temperature in degrees fahrenheit for 20 days during the past month was as follows: 70 76 76 74 70 70 72 74 78 80 74 74 78 76 78 76 74 78 80 76
what is the mode of the temperatures?
78
76
74 and 76

Explanation:

Step1: Recall mean, median and mode formulas

Mean $\bar{x}=\frac{\sum_{i = 1}^{n}x_{i}}{n}$, median is middle - value (or average of two middle - values for even $n$) after sorting data, mode is most frequent value.

Step2: Check first data - set

Data set: $85,19,62,84,93,62,63,83,77,89,43$.
Mean: $\frac{85 + 19+62+84+93+62+63+83+77+89+43}{11}=\frac{760}{11}\approx69.09$.
Sort data: $19,43,62,62,63,77,83,84,85,89,93$. Median is $77$. Mode is $62$.

Step3: Check second data - set

Data set: $60,33,55,68,64,82,78,12,39,39,40$.
Mean: $\frac{60 + 33+55+68+64+82+78+12+39+39+40}{11}=\frac{570}{11}\approx51.82$.
Sort data: $12,33,39,39,40,55,60,64,68,78,82$. Median is $55$. Mode is $39$.

Step4: Check third data - set

Data set: $79,29,72,54,83,57,63,83,75,66,65$.
Mean: $\frac{79+29+72+54+83+57+63+83+75+66+65}{11}=\frac{726}{11}=66$.
Sort data: $29,54,57,63,65,66,72,75,79,83,83$. Median is $66$. Mode is $83$.

Step5: Check fourth data - set

Data set: $55,38,44,39,30,55,58,68,72,78,28$.
Mean: $\frac{55 + 38+44+39+30+55+58+68+72+78+28}{11}=\frac{565}{11}\approx51.36$.
Sort data: $28,30,38,39,44,55,55,58,68,72,78$. Median is $55$. Mode is $55$.

Step6: For the temperature data - set

Data set: $70,76,76,74,70,70,72,74,78,80,74,74,78,76,78,76,74,78,80,76$.
Count frequencies: $70$ appears $3$ times, $72$ appears $1$ time, $74$ appears $6$ times, $76$ appears $5$ times, $78$ appears $4$ times, $80$ appears $2$ times.
The most frequent values are $74$ and $76$.

Answer:

For the first question: C. $79,29,72,54,83,57,63,83,75,66,65$
For the second question: C. $74$ and $76$