Question

1. what is the mean, median, and mode for the following data set: {63, 24, 82, 46, 50, 92, 85, 46, 74, 37}? round the answer to the nearest tenth, if needed.

oa) mean = 59.9, median = 56.5, mode = 46
ob) mean = 58.9, median = 56.5, mode = 46
oc) mean = 59.9, median = 57.0, mode = 63
od) mean = 60.1, median = 50.0, mode = 46
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Explanation:

Step1: Calculate the mean

The mean formula is $\frac{\sum_{i = 1}^{n}x_{i}}{n}$.
Here, $n = 10$ and $\sum_{i=1}^{10}x_{i}=63 + 24+82 + 46+50 + 92+85 + 46+74 + 37=596$.
So, the mean is $\frac{596}{10}=59.6$. Wait, no, let's re - calculate:
$63+24 = 87$, $87+82=169$, $169 + 46=215$, $215+50 = 265$, $265+92=357$, $357+85 = 442$, $442+46=488$, $488+74=562$, $562+37 = 599$.
The mean is $\frac{599}{10}=59.9$.

Step2: Calculate the median

First, sort the data set: $\{24,37,46,46,50,63,74,82,85,92\}$.
Since $n = 10$ (even), the median is $\frac{x_{\frac{n}{2}}+x_{\frac{n}{2}+1}}{2}=\frac{50 + 63}{2}=\frac{113}{2}=56.5$.

Step3: Calculate the mode

The mode is the number that appears most frequently. In the data set $\{63,24,82,46,50,92,85,46,74,37\}$, the number $46$ appears twice, and other numbers appear only once. So the mode is $46$.

Answer:

A. Mean = 59.9, Median = 56.5, Mode = 46