which data set has a mean of 66, a median of 66, and a mode of 83?\n85, 19, 62, 84, 93, 62, 63, 83, 77, 89…

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 $76$